Sift flour with baking powder. In a large bowl, using an electric mixer on medium-high speed, beat butter, sugar and salt until light, about 3 minutes. Beat in eggs and mint extract. Reduce mixer speed to low; beat in flour mixture and 20 crushed peppermint candies just until combined, scraping down sides of bowl as needed.
Turn dough out onto a floured work surface; cut in half. Pat each half into a 1-inch-thick disk. (Alternatively, form disks into 2 or 3 1 1/2- to 2-inch-thick logs.) Wrap in plastic; chill for 1 hour or up to 2 days.
Place racks in upper and lower thirds of oven and preheat to 375°F. Line 2 large baking sheets with parchment. Roll out 1 disk on a lightly floured surface to 1/4-inch thickness. Use cookie cutters to form desired shapes. (If you've formed logs, cut into 1/4-inch-thick slices.)
Using a small metal spatula, carefully transfer cookies to lined baking sheets, spacing about 2 inches apart. Chill for 10 minutes. Bake until lightly browned around edges and firm in center, 12 to 15 minutes, rotating sheets halfway through. Let cookies cool on sheets on wire racks for 5 minutes, then transfer cookies to wire cooling racks to cool completely. Dip each cookie halfway into melted dark chocolate. Sprinkle with additional crushed mints, if desired. Chill until chocolate has hardened. Bring cookies to room temperature before serving.
Repeat with remaining dough, rerolling scraps to use up as much as possible. Decorate cooled cookies with melted chocolate and, if desired, additional crushed peppermints.