I used a 3cm slab, and started from scratch (demo'd the wall). So, my cabinetmaker/fabricator planned from the beginning for the appropriate depth to accommodate my 3cm slab.

In the other half of my kitchen, where we didn't demo the wall, I used a tile b-splash. One of the reasons was that my cabinetmaker/fabricator said it wouldn't look right (I think maybe b/c it would've projected out further than the window casement).

Anyway, after the wall was demo'd, they hung new drywall but didn't float it, and then glued the slab to the wall in the same way that they glued the slabs to the counter.

Pic below

Thank you Madeline616...good info, especially regarding window trim and such! Did not think of that.

I would love to find a 1cm, but a local fabricator tells me he usually only finds 3cm, so if I went that route it looks like some planning is in order to put it everywhere...