Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, creating an overhang on the sides for easy removal. Lightly grease the pan and set aside.
Make the brownie layer: In a medium saucepan (or microwave-safe bowl), combine the chopped chocolate and butter. Heat over low heat or in the microwave in 30-second intervals, stirring until smooth and melted.
Stir in the sugar, espresso powder, and vanilla extract. Let the mixture cool slightly.
Add the eggs: Whisk in the eggs one at a time until fully incorporated and smooth.
Add the flour: Gently fold in the flour, mixing just until no dry streaks remain.
Bake: Pour the brownie batter into the prepared pan and spread evenly.
Bake for 20–22 minutes, or until a toothpick inserted in the center comes out with just a few moist crumbs.
Let the brownies cool completely in the pan.
Make the coconut-pecan glaze: In a small saucepan, combine evaporated milk, butter, egg yolks, and brown sugar.
Cook over medium-low heat, whisking constantly, for about 7–8 minutes, or until the mixture thickens and begins to bubble.
Remove from heat and stir in vanilla, pecans, and coconut. Let the glaze cool and thicken for 5–10 minutes.
Assemble: Once the brownies are cool and the glaze has thickened slightly, spread the coconut-pecan topping evenly over the brownie layer.
Chill: Refrigerate for at least 1 hour (or overnight) to set. Use the parchment sling to lift the brownies from the pan. Slice into squares and serve.