Preheat oven to 350 degrees. Lightly butter bouchon molds and dust with cocoa powder, tapping out excess cocoa. Set bouchon baking mold on a baking sheet.
In a heatproof bowl, melt butter and chocolate in a microwave oven, about 1 1/2 minutes, stirring once. Remove bowl from oven and cool about 10 minutes.
In a medium bowl, whisk together flour, cocoa powder, baking powder and salt and reserve.
In a large bowl, whisk together sugar, egg and vanilla extract until well-combined. Add chocolate-butter mixture and whisk until incorporated. Whisk in flour mixture until just combined.
Scoop 2 tablespoons of batter into well of each mold, filling about two-thirds full. Transfer mold, still on baking sheet, to oven and bake (rotating once halfway through baking time) until tops of chocolate corks are shiny and a toothpick inserted into center comes out with a few crumbs attached, 20 to 22 minutes.