I think granite would work. You can put a pan full of boiling food on granite. You'd have some type of pad over it I assume?

I think you'd want some kind of pad under your clothes. so the countertop material wouldn't really matter.

You can afford an island in your closet and uou are ironing clothes???!!! Take them to the cleaners!!!!!

"You can put a pan full of boiling food on granite."

Not according to the trade association of the natural stone industry. The Natural Stone Institute recommends trivet use on all natural stone. Hot pot marks in granite are rare, but I've seen them.

You're not supposed to place anything hot on any countertop. Do you really think that heat will not have an effect on marble and granite? Heat has an effect on EVERYTHING.

i have the pull out ironing board and as long as you are only doing small touch ups it's great.

For tablecloths and large items a full-size board is required.

For ironing to work well, steam has to be able to go through the ironing surface. Although you probably could iron on quite a few different countertops, (at least synthetics if not pure linen), the quality of your pressing would be low and the amount of effort would be high. Invest in decent tools; they save time and effort.

Soapstone.!!!! HOWEVER,

I have NO idea why you'd want to iron without a pad beneath. If you are talking quick touch ups? Get a pad for the top and iron away. On any top, really

https://www.kohls.com/product/prd-2258095/polder-ironing-blanket.jsp?skuid=99777764&CID=shopping15&utm_campaign=PERSONAL%20CARE&utm_medium=CSE&utm_source=google&utm_product=99777764&utm_campaignid=9733267165&gclid=Cj0KCQjw-uH6BRDQARIsAI3I-UdRFfgkGnx1JtURCHNCFO9_R5rmIBNACoHh2uQCmWdiEICe_Knq_zUaAvM3EALw_wcB&gclsrc=aw.ds

or get a table top. and tuck it away

You could iron on Corian. It isn't the spread-out light heat of ironing that damages tops; it's the concentrated high heat of a curling iron or hot pot that does the damage.

Have you ever tried ironing clothing on a counter top? Probably not or you would be finding room in that huge closet for at least a wall mounted fold down like the last picture that Beverly posted. One of the houses that I grew up in had one like that, although recessed mount, and it works great for clothing. It was much more stable than a fold up ironing board--didn't wobble.

The drawer pull-out ironing boards look like a PITA what with the pull out mechanism & drawer front intruding in the space between you & the ironing board. Places for clothing to catch on as well as the iron cord if using a corded iron. Limited area for clothing to drape off of. But I've not used a pull-out in real life so possibly they are not as user unfriendly as they look.

I agree with the comments that warn against ironing on granite - the natural fissures (seen or unseen) make it vulnerable to thermal shock. Solid surface like Corian and other materials like quartz which has a small resin content could potentially bruise with heat exposure.

One material I've seen that should hold up to heat is thin slab porcelain. This is NOT an inexpensive material. The other alternative is individual porcelain tiles. Find a decorative one that adds a little flair, have the installer use fine grout lines (they could be steam cleaned if needed) with an epoxy grout.

I can't imagine ironing on something like a counter surface if not some kind of wrinkled emergency. Positioning the garment would be just too awkward. My former house had a wired ironing 'center' that folded down from the wall. Adjustable board, power and storage for the iron. The power could be timed to be on 'x' number of minutes, although most irons today seem to have a built in shut off mode where they turn off after so many minutes not in use. Painted the same color as the wall, the 'center' disappeared when door closed and not in use. It seems like it was Nutone and I used it for years.

Sens it all to the cleaners. If it's washed and dried? Fold or hang immediately, not ten hours later. I honestly can't remember the last article of clothing I needed to iron. Oh... two linen shirts in summer. That's it. When I am feeling bored? I iron my sheets. Heavenly.

Soapstone is used in laboratories and is pretty much indestructible. I have a steaming machine that works on hanging garments.

I am intrigued by the idea of doing the ironing in a closet. When I am ironing, I need access to a TV and wine and none of my closets have that.

Whenever I have ironed anything on a surface other than an ironing board, I have always found I needed some sort of padding underneath, which makes the countertop material less relevant. You can choose whatever looks good all the rest of the time that you are not using it as an ironing surface. For me, I would focus on making sure everything is ironed well before being put away and that the closet is designed for the clothes to hang without getting creased. That might not eliminate the need for top-ups, but it certainly minimizes it.

"For ironing to work well, steam has to be able to go through the ironing surface."

Good point, Steam doesn't pass thru those silver ironing board covers that are popular, either. Maybe the OP does not plan to use steam?

I iron on my Corian if I'm in a hurry. Just put a towel down first.

If I had an island in my closet, it would always have something cluttering the top so there wouldn't be room to iron.

Patricia, my mom's laundry room still has the mangler she used to iron napkins, tablecloths, and sheets. Wow, did it do a great job!

I know I wish all the time I had had the sense to get than mangle iron whan my Mom sold her house oh well to late . My Mom even did my Dads dress shirts on that thing the new ones are so small compared to the one my Mom had.

Not that I iron very much, but I find a softer surface allows for the iron to press down in hard to reach places and makes a better job. Since you are designing the closet, suggest a hide away unit whether it be small or large based on your needs. You may also find a better use for the top of the island

they also make fold out / pull out ironing boards that could be installed in the island:

When we built our home we had something similar to these in our bedroom. It's really convenient to have outlet inside. A shelf for my wine is a plus! :-)

https://www.homedepot.com/b/Storage-Organization-Laundry-Room-Storage-Ironing-Boards/Wall-Mounted/N-5yc1vZchd0Z1z0ka2o