Preheat oven to 350°F. Grease and line an 8x8-inch pan with parchment paper.
Brown the butter in a saucepan over medium heat until it smells nutty and golden. Remove from heat. Stir in sugars and cocoa powder. Let cool 5 min.
Add vanilla, then whisk in eggs one at a time until glossy and smooth.
Fold in flour, baking powder, and salt until just combined. Stir in chocolate chips.
Spread into pan and smooth the top. Bake 32–36 minutes or until set with a slight jiggle in the center. Cool completely.
Meanwhile, make the frosting: Beat cream cheese and butter until creamy. Add cocoa powder, powdered sugar, vanilla, and salt. Beat until fluffy, adding milk/cream as needed.
Frost cooled brownies, then chill for 30 minutes for cleaner cuts.