Mich, I'm thinking it could be a WhiteDome lacecap

I think the look is very close to WM too. Its blooms are mostly lacecap, white/yellowish in the middle, with a few white sepals in the perifery of the bloom. I do not expect round white balls from WH though. A "cousin" of Annabelle. I would expect more blooms by now though. ??? But you say it is young still.

Anything else growing nearby such that roots of both plants get comingled? Do you cut the little plants that it produces in order to spread? Any info on fertilizing that you do? How tall is it? Sorry, I could not tell height from the pic.

Ahh, I didn't know about the lacecap varities! I think it very well could be one. I agree it doesn't seem to have many blooms.

Here's another photo for context. It's about 2' tall and 3' wide. It's next to several other perennials, but everything else is also newly planted in the last two years, so I doubt the roots are too extensive yet. We did plant this area new over where we cut down overgrown, mature trees and shrubs when we moved in.

I spread fertilizer granules down in mid-spring this year across the whole bed - nothing special for hydrangeas, just Miracle Grow Shake n' Feed for flowers.

I haven't been cutting any new shoots it sends up to spread. Should I? It doesn't seem like a bush; it grows like my peonies -- dies back completely in the late fall/winter and sends up new shoots in the spring.

It might be a species Hydrangea arborescens, the native form, rather than a cultivar like White Dome or Annabelle. My H. arborescens (Annabelle) sometimes dies down to the ground and sometimes doesn't. It does sucker rather vigorously and if I didn't sometimes rip out a bunch of suckers (the new shoots that cause it to spread) it would take up all the space available and overwhelm the other plants in the bed, an area that's probably 12' or more in all directions. So when it starts getting to large for the space, just remove the suckers.

I agree with NHBabs that it is probably a species or wild hydrangea arborescens. I found a small one growing in a woodsy spot in my yard and it looks very similar to yours. Here are some photos to compare.

http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=k520#AllImages

It won't ever be showy, but perhaps you can appreciate that it's a native plant!

I also have one that has big leaves very green with skimpy blossoms. It was one of my first and was from a neighbor who said it was from her mothers garden in PA. I finally pulled it and moved another one - Buttons and Bows into the space! 8 years waiting for something to happen is long enough for me! lol As we say in our garden .... 'off with her head!'