Microwave butter and chopped chocolate in large bowl, stirring often, until melted, about 1 minute. Whisk sugar, eggs, cocoa, vanilla, and salt into chocolate mixture until smooth. In separate bowl, combine flour and baking powder. Whisk flour mixture into chocolate mixture until combined. Divide batter evenly between two 11-ounce coffee mugs.
Place mugs on opposite sides of microwave turntable. Microwave at 50 percent power for 45 seconds. Stir batter and microwave at 50 percent power for 45 seconds (batter will rise to just below rim of mug). Press 2 chocolate pieces into center of each cake until chocolate is flush with top of cake. Microwave at 50 percent power for 35 seconds (cake should be slightly wet around edges of mug and somewhat drier toward center). Let cakes rest for 2 minutes. Serve.