Preheat oven to 350F and line 2 rimmed baking sheets with parchment.
Cream the butter and sugars until light and fluffy. Add the egg and salt and cream until homogenous.
Add the flour, cocoa powder, baking powder and salt (leave out the powdered sugar) and mix until just combined. Scoop cookies, roll each in powdered sugar and place on one parchment-paper lined cookie sheet. Dent the center of each cookie with your thumb or the back of a tablespoon measuring spoon. Bake for 8-10 minutes and let finish cooling on the cookie sheet.
While the cookies are baking, melt the butter with the mint. Remove from heat and stir in the chocolate. Cool a bit and strain or scoop out the mint leaves.
Roll each cooled cookie into powdered sugar. Fill each center with mint chocolate filling.