Heat the oven to 350°F and prepare a 9x13 inch baking pan by greasing it with butter or cooking spray. Place the room temperature eggs in one bowl. In another bowl, sift the flour, cocoa powder, salt, and espresso powder together to eliminate lumps and ensure the cocoa and espresso are evenly distributed throughout. Have all ingredients measured and ready.

Using a double boiler or microwave in 30-second intervals, melt 1 cup butter with the chocolate chips, stirring between intervals to prevent scorching. Allow the melted mixture to cool for 5 minutes. Add this cooled chocolate mixture to the eggs along with both the granulated sugar and brown sugar, plus the vanilla bean paste. Whisk energetically for approximately 2 minutes until everything is well blended and the mixture appears slightly aerated. Gently fold in the sifted dry ingredients until just incorporated, being careful not to overmix so the brownies remain tender.

Transfer the brownie batter into the greased pan and use a spatula to spread it evenly across the bottom. Bake for 35 to 40 minutes, checking doneness by inserting a toothpick in the center—it should come out with a few moist crumbs clinging to it. The brownie edges should begin pulling away from the pan sides. Remove from oven and place on a wire rack to cool completely, which will take about 1 hour, before applying frosting.

As the brownie cools, prepare the frosting by beating the softened butter with the cream cheese for 2 to 3 minutes until the mixture becomes light and fluffy. Philadelphia brand cream cheese is recommended for creating a more stable, smoother frosting. Add the sifted icing sugar gradually in several batches, mixing on low speed after each addition to prevent sugar from flying everywhere. Mix in the vanilla bean paste, milk, and a pinch of fine sea salt, then continue beating until the frosting is smooth and spreadable with a thick but not stiff consistency.

Once the brownie is completely cool, spread approximately two-thirds of the prepared frosting evenly over the top using an offset spatula or butter knife. In one corner of the frosted brownie, arrange the blueberries in a tight grid pattern of 8 rows by 7 rows to represent the stars of the flag. On the remaining portion of the brownie, create horizontal stripes by arranging the raspberries in parallel rows, leaving 1 to 2 inches of frosted space visible between each raspberry row.

Place the remaining one-third of frosting into a piping bag fitted with either a small round or star tip. Pipe lines of frosting in the spaces between each raspberry row to clearly define the stripes and give the cake a polished, finished appearance. Refrigerate the completed decorated cake for at least 30 minutes to allow the frosting to firm up, which will make cutting and serving much cleaner. Slice into squares and serve.