Prepare pan: Adjust oven rack to middle position and heat oven to 350 degrees. Line 8-inch-square baking pan with heavy-duty aluminum foil, making sure that foil is tucked into all corners and that at least 1 inch overhangs top on all sides.
Make batter: Melt butter and chocolate together. Set aside to cool slightly. Combine flour, baking powder, and salt in small bowl. Whisk sugar and eggs together in large bowl. Stir chocolate mixture and vanilla into egg mixture. Stir in flour mixture until just incorporated.
Assemble: Set 1 cup brownie batter aside. Pour remaining batter into prepared baking pan. Arrange Peppermint Patties on top of batter, leaving about 1/2 inch between each piece. Smooth reserved 1 cup batter over candy.
Bake: Bake until just set in center, 30 to 35 minutes. (Cake tester won’t work because of candy.) Cool completely in pan on wire rack, about 2 hours. Grasp overhanging foil on sides of pan and transfer brownies to cutting board. Cut into 36 pieces and serve. (Brownies will keep at room temperature in airtight container for up to 3 days. )