Heat oven to 350°F. Grease a 9x13-inch pan and line with a parchment sling.
Melt butter with chopped chocolate in a saucepan over low heat, stirring until smooth. Let cool 5 minutes.
Whisk granulated sugar, brown sugar, eggs, and vanilla in a large bowl until glossy and slightly thick.
Stream the warm chocolate mixture into the egg mixture while whisking until combined.
Sift in flour, cocoa, salt, and espresso powder. Fold just until no dry streaks remain.
Spread batter into the pan and smooth the top. Tap the pan to level.
Bake 28–35 minutes, until edges are set and a tester shows a few moist crumbs. Cool completely in the pan.
Make frosting: Whisk evaporated milk and egg yolks in a medium saucepan. Add butter and brown sugar.
Cook over medium heat, stirring constantly, until thickened and bubbling, 8–10 minutes.
Remove from heat. Stir in vanilla, salt, coconut, and pecans. Cool until spreadable, about 10 minutes.
Spread frosting over cooled brownies. Chill 20 minutes to set the top.
Drizzle with melted chocolate and sprinkle toasted coconut, if using. Lift out and slice into 16 squares.