Preheat your oven to 350°F and grease a 9x13 inch baking pan with butter or cooking spray. Separate your room temperature eggs into a bowl. Sift together the flour, cocoa powder, salt, and espresso powder in a separate bowl to remove any lumps and ensure even distribution of the cocoa and espresso—this prevents pockets of concentrated flavor in the finished brownie. Have all your ingredients measured and ready before you begin mixing.
Melt 1 cup butter with 2 cups chocolate chips using a double boiler or microwave in 30-second intervals, stirring between each interval to avoid scorching. Let the mixture cool for 5 minutes, then add it to your eggs along with both sugars (1/3 cup sugar and 1 1/2 cups brown sugar) and vanilla bean paste. Whisk vigorously for about 2 minutes until the mixture is well combined and slightly fluffy. I like to use an extra egg yolk whisked in separately to ensure the richest brownie, but it's optional. Fold in the dry ingredient mixture from Step 1 until just combined—don't overmix, as this keeps the brownies tender.
Pour the batter from Step 2 into your prepared 9x13 inch pan, spreading it evenly with a spatula. Bake for 35-40 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs—don't overbake, as the residual heat will continue cooking the brownie after it leaves the oven. The edges should pull slightly away from the pan sides. Remove from the oven and let cool completely on a wire rack (about 1 hour) before frosting.
While the brownie cools, beat 1/2 cup softened butter with 8 oz cream cheese until light and fluffy (about 2-3 minutes). I prefer Philadelphia brand cream cheese because it creates a more stable, less grainy frosting than store brands. Gradually add 4 cups sifted icing sugar in batches, beating on low speed after each addition to avoid a sugar cloud. Add 1 teaspoon vanilla bean paste, 2 tablespoons milk, and a pinch of fine sea salt, then beat until smooth and spreadable. The frosting should be thick but not stiff.
Spread about two-thirds of the frosting from Step 4 evenly over the cooled brownie using an offset spatula or butter knife. Starting in one corner, arrange 1 cup blueberries in a tight 8x7 grid pattern to represent the stars on a flag. Then create horizontal stripes across the remaining brownie by arranging 2 cups raspberries in rows with about 1-2 inches of space between each row, leaving frosting visible between the raspberry lines.
Transfer the remaining one-third of frosting from Step 4 to a piping bag fitted with a small round or star tip. Pipe lines of frosting between each raspberry row to define the stripes and create a polished presentation. Chill the completed cake for at least 30 minutes before cutting to allow the frosting to set and make slicing cleaner. Cut into squares and serve.