Preheat your oven to 350°F (175°C). Grease and line a 9x13-inch baking pan with parchment paper, leaving some overhang for easy removal.
In a large mixing bowl, combine the melted butter and granulated sugar. Stir until well combined. Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
In another bowl, whisk together the flour, cocoa powder, salt, and baking powder. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Pour the brownie batter into the prepared baking pan and spread it evenly. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Let the brownies cool completely in the pan.
Once cooled, lift the brownies out of the pan using the parchment paper. Cut the brownies into squares or rectangles, depending on your desired sandwich size.
Take one brownie piece, add a scoop of softened ice cream on top, and then place another brownie piece on top to create a sandwich. Press gently to adhere.
Repeat with the remaining brownies and ice cream. For best results, freeze the sandwiches for at least 1 hour before serving to firm them up.