Lightly butter each cavity, then chill 5 min to set the fat. Dust cavities with rice flour (or AP flour); tap out the excess. (Best release + minimal clogging of designs.)

Beat butter + 1 cup sugar on medium-low until smooth and slightly fluffy, 1–2 min. Beat in eggs, one at a time, then vanilla; scrape bowl. In a separate bowl, whisk flour, cocoa, baking powder, salt, cornstarch. Add dry mix to wet; mix on low just until combined. Dough will be soft/sticky. Cover and chill until scoopable and firm, 60–90 min (or 30 min in the freezer).

Preheat oven to 320–325°F (160–165°C). Scoop pieces sized to your cavities (about 1 Tbsp / 20 g for small, 1.5 Tbsp / 30 g for deeper). Roll each piece in granulated sugar (helps keep powdered sugar from melting), then thickly in powdered sugar. Quickly press the coated dough into a cavity, pushing from center outward to fill the pattern; avoid air pockets. Level the backs by scraping a flat edge (bench scraper/offset spatula) across the rim so the dough is flush and even.

Chill the filled mold 15–20 min (or freeze 8–10 min). This preserves edges and prevents the sugar from dissolving. Bake until edges look set, surfaces are matte with visible cracks, and centers spring back lightly: Shallow cavities: 12–14 min, Deeper cavities: 15–18 min, Cookies should be mostly pale on the sugar, not browned.

Cool the pan on a rack 5–7 min. Invert and tap the pan edge to release. If any cling, ease gently with a thin plastic/wood tool (avoid metal on nonstick). Cool completely on a wire rack.