We have exposed a brick wall in our kitchen (big mistake, if I could do it over I would have kept the plaster) that has finally been pointed in a few places where the mortar was missing. The new kitchen floor has also been installed, so now I am ready to install my new baseboard.

We are matching the trim in the rest of the house, so the baseboard is 6" poplar, 1" thick, with a separate cap piece and will be painted.

What is the best way to attach this to the exposed brick wall? The old trim had been nailed to wooden "shims" that had been wedged in between the bricks before the plaster had been applied. I am doubting I could follow the same method and get it to rest relatively flat against the exposed brick. I was thinking of a combination of construction adhesive and tapcon screws, but I was hoping someone here might have a better (or easier) idea!