Make the caramel: line a baking sheet with parchment paper. In a large pot over medium heat, cook 1/3 cup granulated sugar, stirring occasionally, until the sugar melts and becomes a golden caramel (about 8 minutes). Remove the pot from the heat and whisk in the 2 tablespoons salted butter chunks until combined. Stir in 1/4 cup heavy cream, return the pot to medium heat, and cook, stirring, until the caramel thickens and coats the back of a spoon (about 5–8 minutes). Remove from heat, stir in a pinch of flaky sea salt, pour the caramel onto the prepared parchment, and freeze for 20 minutes to harden.
While the caramel chills, preheat the oven to 350°F and line a 9×9-inch square pan with parchment paper.
Melt the batter chocolate: in a microwave-safe bowl, combine the 1 1/2 sticks (12 tablespoons) salted butter and 1 cup of the semi-sweet (or milk) chocolate chips. Microwave at 30-second intervals, stirring between intervals, until the mixture is melted and smooth.
Stir sugar and flavorings into the melted chocolate: add 1 cup granulated sugar, 1 tablespoon instant coffee/espresso, 1 tablespoon Kahlúa, and 2 teaspoons vanilla extract to the warm chocolate mixture; stir until evenly combined.
Prepare and temper the eggs: in a small bowl, whisk the 3 large eggs briskly for about 1 minute until slightly bubbly. To avoid scrambling, temper the eggs by gradually adding a small amount of the warm chocolate mixture to the whisked eggs while stirring, then pour the tempered egg mixture back into the chocolate bowl and stir until combined.
Add the dry ingredients: add 1/3 cup all-purpose flour, 1/3 cup unsweetened cocoa powder, 3/4 teaspoon baking powder, and 1/4 teaspoon kosher salt to the chocolate-egg mixture. Stir just until combined (do not overmix).
Fold in remaining chocolate chips: stir in the remaining 1/2 cup chocolate chips until evenly distributed.
Assemble the brownies in the pan: spread half of the batter evenly into the prepared 9×9 pan. Use a spoon to dollop the 1/2 cup Nutella in separate spoonfuls across the batter. Spoon the remaining batter over the Nutella dollops, smoothing lightly with a spoon — it’s okay if the top layer doesn’t fully cover all the Nutella.
Add the caramel pieces: remove the caramel from the freezer, break or cut it into pieces, and press the pieces into the top of the brownie batter as desired (you may not need all the caramel pieces).
Bake and finish: bake the brownies at 350°F for 28–30 minutes, or until the brownies are just set. Remove from the oven and let the brownies cool in the pan until they are firm enough to lift out on the parchment (or cut and serve warm if you prefer).