Preheat the oven to 350°F and line baking sheets with parchment paper.
Melt chocolate and butter in a heatproof bowl over simmering water, stirring until smooth.
Whisk eggs, sugar, and vanilla until glossy, then stir in melted chocolate.
Mix flour and baking powder separately; fold into wet ingredients to form a thick dough.
Combine peanut butter and powdered sugar until smooth; roll into 1-inch balls.
Scoop 1½ tablespoons of dough per cookie, press a peanut butter ball in the center.
Bake for 10 minutes until edges are firm and centers soft.
Melt semisweet chocolate and spoon over cooled cookies.
