Preheat oven to 350° F. Butter a 9-by-13-inch pan, and then add a layer of parchment paper, leaving the edges long enough to lift the brownies out of the pan once cool or easier slicing. Butter the parchment paper, pressing it to adhere smoothly to the pan.

Melt butter in a medium saucepan over medium heat. Add sugar and stir to combine. Continue to cook until the mixture is hot but not bubbling; it will become shiny as you stir it. Transfer mixture to the bowl of a standing electric mixer. Stir in cocoa, salt, baking powder, and vanilla. Add the eggs, one at a time, beating until smooth. Add flour and chocolate chips, stirring until well combined.

Scrape the batter into the prepared pan, spreading it as evenly as you can; it will be thick and glossy.

Bake for 28 to 30 minutes, until a toothpick inserted in the center comes out clean. Remove from the oven. Once cool, gently lift the brownies from the pan and transfer to a cutting board. Cut into squares or use large cookie cutters to make shapes.

To make brownie ice cream sandwiches, slice brownie squares or shapes in half lengthwise. If the brownies are still slightly warm, place slices in the freezer for about 15 minutes to cool them down. Scoop small mounds of vanilla ice cream onto the bottom half of each pair (do not pre-thaw the ice cream). Gently spread the ice cream to the edges of each brownie. Add brownie tops over the ice cream and press each sandwich together gently. Serve immediately or place in an airtight container and freeze until ready to serve.