In a bowl, whisk together flour, baking powder, and salt. In another bowl, beat butter with sugar until pale and fluffy, about 2 minutes. Beat in eggs and vanilla. Add flour mixture, beating just until combined. Divide dough in half, transfer each to plastic wrap, form into disks, wrap tightly, and refrigerate until firm, at least 2 hours and up to 3 days (or freeze up to 1 month).

Preheat oven to 325 degrees, with racks in upper and lower thirds. Let 1 disk of dough stand at room temperature until soft enough to roll, about 10 minutes. On a lightly floured work surface, roll out to a scant 1/4 inch thick. Stamp out tree shapes with an approximately 4-inch-tall cookie cutter, transferring cutouts to parchment-lined baking sheets as you work. Use a star-shaped aspic cutter to stamp out tree toppers from dough scraps. Repeat with remaining disk of dough. Freeze cutouts until firm, about 15 minutes.

Bake, rotating rack positions halfway through, until cookies are set and edges turn golden, 15 to 18 minutes. Let cool on sheets 5 minutes, then transfer to wire racks; let cool completely.

Transfer melted chocolate to a pastry bag fitted with a small, plain tip, such as Ateco #2 (or use a small freezer bag, and snip the tiniest possible hole in one corner). Starting at top of each tree, drizzle chocolate in a random back-and-forth pattern, then adhere candies intermittently to mimic string lights. Pipe a small dot of chocolate at very top of tree, and adhere a cookie star. Let stand at room temperature until chocolate sets, about 4 hours; or refrigerate just until set, about 15 minutes. (Do not keep cookies in refrigerator.) Store in an airtight container at room temperature, between sheets of parchment, up to 1 week.