Preheat the oven to 350F. Thoroughly coat an 8"x8" baking pan with nonstick spray and set aside.
Put butter, chocolate and cocoa powder into a heatproof bowl set over a saucepan of simmering water (about an inch of water). This is a makeshift double boiler, which will ensure the chocolate melts without burning or changing consistency. Stir constantly until butter and chocolate have melted and the mixture is smooth and uniform in color and consistency. Remove from heat and set aside to cool slightly.
Meanwhile, beat the eggs together with the sugar and vanilla until pale, using an electric mixer, or a sturdy whisk. This should take several minutes. Slowly add chocolate mixture in a thin stream, whisking continuously to incorporate. Don't dump it all in at once because any residual heat in the chocolate could start to cook the eggs.
Now add the dry ingredients (flour, baking powder, and salt) all at once and beat until just combined. Do not overbeat, but use a rubber spatula to scrape the sides of the bowl and turn the batter over a few times to make sure everything is incorporated.
Pour half of the batter into prepared pan. Evenly space Andes mints on top of the layer, in three rows of four mints. Then cover with the remaining half of the batter and carefully smooth with a rubber spatula to evenly distribute and flatten the batter. No Andes should be showing.
Bake for 25 minutes, or until a knife inserted into the center comes out clean-ish (no wet batter, but some crumbs may stick to it). Remove pan from oven and allow to cool completely before cutting.
Makes 16 brownies. Store in an airtight container for up to 5 days, or in the freezer for 3 months.