Microwave butter and 8 ounces chocolate in microwave-safe bowl, stirring every 30 seconds until smooth. Cool 10 minutes.
Beat sugar, eggs, and vanilla in large bowl 2-3 minutes until thick and pale.
Mix cooled chocolate into eggs thoroughly.
Separately whisk flour, cocoa, baking powder, and salt.
Fold dry into chocolate just until combined; add remaining 4 ounces chocolate.
Cover; refrigerate at least 1 hour or up to overnight until firm enough to handle.
Heat oven to 350°F; line sheets with parchment. Put powdered sugar in shallow bowl.
Roll chilled dough into 1½-inch balls; generously coat with powdered sugar.
Place 2 inches apart; bake 11-12 minutes until edges set and centers slightly underbaked. Cool on sheet 5 minutes; transfer to rack.