Preheat oven to 350°F. Lightly butter an 8x8-inch baking dish. Line with two overlapping strips of parchment paper, leaving overhang on all sides for easy removal. Lightly butter the parchment.
In a medium bowl, stir together melted butter and sugar until combined. Add eggs, vanilla, and salt. Stir until smooth, then fold in cocoa powder and flour just until combined.
12 Tbsp unsalted butter, 1 ½ cups sugar, 2 eggs, 2 tsp vanilla extract, ½ tsp salt, ¾ cup cocoa powder, ½ cup all-purpose flour
Spread half the brownie batter into the prepared pan.
Spoon about ½ cup salted caramel over the batter, spreading gently but leaving a small border around the edges.
½ cup of the salted caramel
Top with remaining brownie batter, covering as much caramel as possible.
Bake for 30 minutes at 350°F. Reduce heat to 325°F and bake another 10 minutes, or until the center is just set and a knife comes out with a few moist crumbs.
Cool completely before cutting into 9 brownies. Drizzle with extra caramel and sprinkle with flaky sea salt, if desired.
Coarse salt for sprinkling on finished brownies