Heat the oven to the temperature specified on the brownie-mix package, usually 350°F. Line a 13 x 9-inch baking pan with foil or parchment, leaving an overhang on the sides, and lightly grease the lining.

Prepare the fudge brownie batter according to the directions on the specific package, using the listed water, vegetable oil, and eggs. Mix only as directed so the finished brownies stay fudgy.

Arrange the six broken graham-cracker sheets across the bottom of the prepared pan. Pour the brownie batter evenly over the crackers and gently spread it into the corners.

Bake according to the package directions, usually checking at 25–30 minutes. The center should be nearly set, and a toothpick should come out with moist crumbs rather than wet batter.

Scatter 1 to 1 1/2 cups of mini marshmallows over the baked brownie surface. Return the pan to the oven for about 2–5 minutes, just until the marshmallows puff and begin to brown.

For deeper color, broil the marshmallows for only a few seconds while watching constantly. Remove the pan immediately and add the red, white, and blue candies or sprinkles while the topping is still warm.

Cool the brownies completely for 30–60 minutes before cutting. Use the foil or parchment overhang to lift the slab from the pan, then cut it into 24 squares with a lightly greased knife.