Cream the butter and sugar until light and fluffy (about 5 minutes). Mix in the almond extract.
In a separate bowl, sift together the flour, almond meal, matcha powder, and salt (if adding).
Dump the dry ingredients into the wet ingredients and mix until just incorporated. Add the chopped almonds until evenly mixed into dough.
Put the dough into the refrigerator for 30 minutes, while your oven pre-heats to 350 degrees F.
On a lightly floured surface, or parchment paper, roll the dough to a thickness of about 1/4" and use a small (~2" diameter) cookie cutter to cut cookies. Continue re-rolling dough and cutting cookies until no dough remains. Place cookies on a cookie sheet about 2" between each cookie.
Bake cookies for 12-14 minutes, turning the cookie sheet about halfway through. Once out of the oven, allow cookies to rest on the cookie sheet for two minutes, then transfer to a rack to cool completely. Store cookies in an airtight container.