Preheat your kitchen oven to 350°F (180°C) and line an 8-inch (20cm) square baking pan with parchment paper, leaving an overhang for easy removal.
In a large mixing bowl, whisk the warm melted butter, white granulated sugar, and packed light brown sugar together until completely combined.
Add the instant coffee granules and vanilla extract, welcoming them into the warm fat until fully dissolved.
Crack in the room-temperature eggs one at a time, beating the mixture aggressively for one full minute until the batter turns thick and shiny.
Sift the all-purpose flour, Dutch cocoa powder, and fine sea salt directly into the wet base, then fold gently with a rubber spatula just until the dry spots vanish.
Pour the thick chocolate batter into your prepared baking pan, spreading it evenly into the corners.
Bake for exactly 22 minutes until the edges are set but the center remains slightly soft to the touch.
Remove from the oven and let the pan cool completely on a metal wire rack before attempting to frost.
To make the frosting, beat the softened butter in a stand mixer for 2 minutes until light and creamy.
Gradually add the powdered sugar, cocoa powder, cooled brewed espresso, and heavy cream, whipping on high speed until fluffy.
Spread the mocha frosting evenly across the cooled brownie slab, slice into 16 squares, and serve.