Preheat your oven to 350°F and line a mini muffin tin with paper liners (you'll need about 24). Melt the butter in a large bowl over low heat or in the microwave for about 90 seconds. The butter should be completely melted but not sizzling.
Stir in both sugars until they're completely combined with the melted butter. This should take about 30 seconds and look kinda crumbly. Now crack in your 3 eggs one at a time, stirring well after each addition so they blend smoothly into the mixture.
Add the vanilla extract and stir it in completely. Then sprinkle the cocoa powder over the top and fold it in gently until no dry cocoa streaks remain. The batter should look thick and fudgy at this point.
In a separate small bowl, whisk together the flour, baking powder, and salt. Pour this dry mixture into your chocolate batter and stir just until combined — don't overmix or your brownies will get tough and cake-like. Fold in the chocolate chips last.
Fill each mini muffin cup about two-thirds full with batter using a small ice cream scoop or spoon. I always use a scoop because it keeps the bites uniform and they bake evenly. Fill any empty cups halfway with water so they bake at the same temperature.
Bake for 18-22 minutes until a toothpick inserted in the center comes out with just a few moist crumbs (not wet batter). The tops should look set but still have a tiny bit of jiggle when you shake the pan gently. Mine always bakes perfectly at 20 minutes, but ovens vary so check at 18.
Let the brownie bites cool in the pan for 5 minutes, then carefully pop them out and transfer to a wire rack. Once completely cool (about 30 minutes), top each bite with a dollop of whipped topping and sprinkle with nongelatin rainbow sprinkles. This is where they transform into patriotic brownie bites that look almost too pretty to eat.