Whisk the flour, cocoa powder, baking powder, and salt in a medium bowl to combine. Set aside.

Beat the granulated sugar and butter in the bowl of a stand mixer fitted with paddle attachment on medium-high speed until light and fluffy, about 4 minutes. Add egg and vanilla and beat to incorporate, about 1 minute. Reduce speed to low and add dry ingredients. Beat just until dough comes together. Alternatively, dough can be mixed in a large bowl using a hand held mixer.

Divide the cookie dough in half and pat each into a disk; wrap tightly in plastic. Chill just long enough so that the dough is rollable and no longer sticky, about 30 minutes.

Working with one disk at a time, roll out the dough between 2 sheets of parchment paper until ⅛" thick. Slide onto baking sheets, still sandwiched between parchment, and chill until very firm, about 1 hour.

Place rack in the center of the oven. Preheat oven to 350°F.

Carefully peel away top sheets of parchment from dough and punch out cookies with larger cutters. Punch out centers of half of cookies with smaller cutters. Carefully transfer whole cookies with a spatula to a parchment-lined baking sheet, spacing 1" apart. Sprinkle remaining cut-out cookies with sanding sugar, then transfer to another parchment-lined baking sheet. Bake cookies until edges are set, 7–10 minutes. The cut-out cookies will require slightly less time in the oven, 6-9 minutes.

Let cool on baking sheets. Repeat process with scraps (if necessary, chill dough again before punching out shapes).

Melt chocolate and tahini in a bowl in a microwave in 20-second bursts, stirring after each, until chocolate is melted (or melt in a heatproof bowl set over a saucepan of simmering water; do not let bowl touch water). Stir to combine. Spread filling over whole cookies not quite to the edge; top with matching cut-out cookies.

Do Ahead: Cookies can be assembled 5 days ahead. Store airtight at room temperature.