Combine butter and bittersweet chocolate in a small microwave-safe bowl. Microwave at HIGH 45 seconds, stirring every 15 seconds. Stir until smooth. Cool to room temperature.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 4 ingredients (through baking soda) in a large bowl; stir well with a whisk.
Combine granulated sugar, milk, vanilla, and eggs in a bowl; stir with a whisk until well combined.
Add butter mixture and milk mixture to flour mixture, stirring just until combined. Gently stir in chocolate chips. Divide batter evenly among 12 lined muffin cups. Bake at 425° for 5 minutes. Reduce oven temperature to 375° (do not remove muffins from oven). Bake at 375° for 10 minutes or until a wooden pick inserted in center comes out with moist crumbs clinging. Cool in pan on a wire rack 5 minutes. Remove from pan; cool completely on wire rack. Sprinkle with powdered sugar, if desired.