Is the wood cracked or just the finish? If the finish is cracking, sand it down smooth before painting. If a layer of veneer (if it is veneered) is cracking, you could cover the side with a 1/4 thick piece of plywood with a smooth finished side. Since you are painting, it does not need to be the same as the wood of the cabinet. It looks from the picture that the face frame extends about 1/4 inch beyond the side and would cover any additional material added to the side.

If it fits your style, a 1/4 width beadboard is also possible. You will need to cut any material the correct dimensions. Some home center stores will cut material for you - just be sure your measurements are right on and they cut it correctly. Since you are painting, a small area that isn't snug or small gap could be filled with wood filler or caulk.

This is a paint grade wood side panel - it would need to be cut in half length wise - giving you 2 12 x 84 pieces:

https://www.menards.com/main/home-decor/home-accessibility/kitchen-laundry-accessibility/shop-all-kitchen-cabinets/quality-one-trade-24-x-84-unfinished-maple-utility-cabinet-panel/ueputilitypnlmaple/p-1444451718635-c-14242.htm?tid=-3684074819332101839&ipos=18

Since it's a pantry, maybe a fun idea would be to add a chalkboard? I don't know how casual your family is but it maybe a fun idea to make a grocery list or menu. Since the cabinets will be white you could place white framing around it would look nicer.

show me where it's cracked. I can't see from that pic.

that's a nice oak cab. it would look so good if you did a real milk paint on it. it's the perfect wood piece to do it to. don't do a reg cabinet paint. this is a vintage piece and needs a vintage milk paint. I'd love to get my hands on that!

what colors do you like for it? NO to the chalkboard

do you have any Titebond wood glue?

Reconsider painting your oak pantry cabinet.

Your pantry is a separate cabinet -- a piece of oak furniture -- not a built in as kitchen cabinets are -- so it doesn't need to be painted match your white painted kitchen cabinets unless you just want that.

Before you do any painting, see if you can address the cracking. If the cracks appear to be only in the finish -- polyurethane? -- and not in the wood, remove all the finish and sand. If the cracks are in the wood, try using an oil to add moisture back to the wood. Apply it several times and allow it to be absorbed into the wood each time before adding more. Scroll down on this page for list and "how to":

https://www.diynatural.com/wood-finishes-natural/

Natural Wood finishes include:

Linseed Oil

Tung Oil

Walnut Oil

Sunflower Oil

Jojoba Oil

Mineral Oil

Beeswax

Soy Wax

Carnauba Wax

http://theprovince.com/life/furniture-care-part-4-oiling-wood-furniture

If you want a cork or chalk "board", consider creating one on the INSIDE of your cabinet rather than outside.

the cracks are the veneer lifting. using oil will not fix those. they need glue

take a bit of the wood glue and use your finger or a syringe to push the glue into those cracks. (your going to have to lay this piece over on it's side) and put something very heavy on it to press it down. if you have a wood clamp, even better. when it's dry, (give it a day), give it a good sanding to smooth it out. Wipe off any excess glue w/mineral spirits before it dries.

Jacquie,,,this is a really cool cab w/some great oak grain. If you want it to look like your white kitchen cabinets, then just order a pantry cabinet to match. Otherwise, treat this to a special paint job that will benefit it's unique and vintage look. With that heavy grain you have, it's never going to look new and smooth like your kitchen cabinets. Treat it as a separate, vintage piece, next to your new cabinets

what I would love to do is milk paint. first I'd deepen the stain color and do a quick staining w/a dark walnut gel stain. it dries fast. Then I'd pick a color (i'm going to show you blues and greens because that's the only colors I could find in the type of paint job I'd do to this) in the regular milk paint. (comes in a powder and you mix w/water).

I did an oak cab while back w/blue and teal. looks like this on the first coat

I gave it two coats, did some fine sanding and coated it w/tung oil.

I did another cabinet in blues too

you can use a white milk paint, or even a black would look great.

imagine the darker stain coming through w/black (not quite as rustic as this turquoise, ) ignore the colors,,unless you like the blue,,,just trying to give you an idea of the stained wood coming through the milk paint in varying degrees.

the black or a navy and the darker stain on the wood, would look something like this

Jacquie, that came out Great!!

nice Jacquie!