Preheat the oven to 325 degrees F. Spray an 8-inch square baking dish with cooking spray. Line the baking dish with parchment paper and spray the parchment with cooking spray.
Whisk together the flour, baking powder and salt in a small bowl. Set aside.
Melt the butter, unsweetened chocolate and 1/2 cup of the semisweet chocolate chips in a medium heatproof bowl over a double boiler. Remove from the heat. Stir in the sugar, instant espresso and vanilla until the mixture is smooth.
Stir in the beaten eggs and mix just until combined. Stir in the flour mixture until fully combined, and then pour the batter into the prepared baking dish and spread it smooth. Scatter the remaining 1/2 cup semisweet chocolate chips evenly over the top.
Bake until the brownies have puffed and a toothpick inserted near the center comes out with moist crumbs, 46 to 48 minutes. Remove the brownies from the oven and allow to cool before cutting.
Chilling your brownies in the refrigerator for at least 1 hour makes for easier cutting.