Preheat oven to 350 degrees F. Line a baking sheet with parchment paper, and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream together butter and sugar. Add eggs, one at a time, beating well after each addition and scraping down the sides. Beat in extract.
In a medium mixing bowl, combine the flour, peppermint candy, baking powder, and salt. Gradually add to creamed mixture, beating until blended (dough will be sticky).
Divide dough in half. Shape each portion into a 12-by-2-1/2-inch rectangular slab arranged side by side lengthwise on the prepared baking sheet, leaving space in between so allow for expansion. Straighten and smooth out the tops and edges. Bake for 25 to 30 minutes or until light golden brown.
Carefully remove to wire racks (use a spatula on each end to carefully lift and move). Cool for 15 minutes. Transfer to a cutting board and cut diagonally into 1/2-inch-thick slices with a sharp knife perpendicular to the board.
Place cut side down on parchment-lined baking sheets (you'll need 2 baking sheets for this step, or bake 1 sheet at a time reusing the same sheet pan). Bake for 12 to 15 minutes or until firm. Remove to wire racks to cool.