In a mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add 1 cup granulated sugar, baking powder, and salt. Beat until combined, scraping bowl occasionally. Beat in egg and vanilla until combined. Beat in as much flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
Divide dough in half. Stir melted chocolate into one dough portion. Stir chocolate mint baking pieces and peppermint extract into remaining dough portion. Divide each dough portion in half. Cover dough and chill for at least 1 hour or until easy to handle.
Roll each peppermint dough portion into a 9-1/2x6-inch rectangle on a piece of waxed paper. Roll each chocolate dough portion into a 9-1/2x6-inch rectangle on waxed paper. Use waxed paper to invert one chocolate dough rectangle on top of one peppermint dough rectangle; remove top layer of waxed paper. Roll up dough, jelly-roll style, starting from a long side and using bottom layer of waxed paper to help lift and roll dough. Discard waxed paper. Pinch edges to seal. Wrap dough roll in plastic wrap. Repeat to make a dough roll with remaining chocolate and peppermint dough rectangles. Chill dough rolls in the refrigerator for 1 to 2 hours or until very firm.
Preheat oven to 375 degrees F. Lightly grease a cookie sheet; set aside. Unwrap dough rolls; reshape, if necessary. Cut dough rolls crosswise into 1/4-inch slices. Place slices about 2 inches apart on prepared cookie sheets. If desired, sprinkle with edible glitter.
Bake for 6 to 8 minutes or until edges are firm and just starting to brown. Transfer cookies to wire racks and let cool. Stack cookies in canister; cover.***