Adjust oven rack to middle position and heat to 350°F.
Make foil sling for an 8 inch square baking pan, and grease the aluminum foil and sides of the pan.
Whisk flour, baking powder, and salt together in a bowl.
Microwave butter and chocolate in second bowl at 50 percent power, stirring occasionally, until melted and smooth, 2 to 3 minutes; let cool slightly.
Whisk sugar and eggs together in large bowl.
Add vanilla and chocolate mixture and whisk until combined.
Add flour mixture and stir until just incorporated.
Pour all but 1 cup batter into the prepared baking pan. (This is about half of the batter)
Spread an even layer of peppermint patties ½ inch apart on top of the batter.
Spread remaining batter over patties.
Bake until just set in the center, 30 to 35 minutes, rotating pan halfway through baking.
Let bites cool in pan for 2 hours on a wire rack.
Using foil overhang, lift bites out of pan. Cut into 36 pieces before serving.