Prepare your workspace by lining a 9x13-inch baking sheet with parchment paper, letting some hang over the edges.

Combine unsalted butter, granulated sugar, and light brown sugar in a small saucepan over medium heat and stir occasionally until the butter melts and sugars dissolve, about 2 minutes.

Without stirring, let the mixture bubble gently for 6 to 8 minutes, until it reaches 300 to 310°F on a candy thermometer (hard-crack stage).

Remove the saucepan from heat and quickly stir in sea salt and vanilla extract.

Immediately pour the hot caramel onto the prepared baking sheet and spread it evenly with an offset spatula.

Place chopped chocolate, cocoa powder, and espresso powder into a medium microwave-safe bowl and melt in 30-second bursts, stirring between each, until smooth, about 60 to 90 seconds total.

Pour the melted chocolate over the warm caramel layer and spread evenly with an offset spatula.

Let the brittle cool completely at room temperature for at least 2 hours, or refrigerate for 30 to 45 minutes to speed up setting.

Once hardened, use the parchment overhang to lift the brittle onto a cutting board and break it into pieces by hand or cut into uniform rectangles with a knife.