Preheat the oven to 350. To make the brownies, start by browning your butter — add the butter to a pot or large pan over medium heat. Let the butter melt and begin to bubble. After a couple minutes, it will foam up a lot, then the foaming will subside, and you’ll be left with brown, nutty smelling butter!
Take off the heat and add chocolate chips, sugar, and brown sugar. stir until the chocolate is melted. Let the mixture cool for several minutes, then add the vanilla, then the eggs one at a time, stirring quickly after adding each one.
Sift in the dry ingredients and stir until just combined. Pour the brownie batter into a greased or lined 9x13 inch pan. Cook at 350 for 38-42 minutes.
While the brownies are cooling, make the topping. Add the evaporated milk, egg yolks, brown sugar, and butter to a large pan or pot over medium heat. Let it cook until it starts to boil, stirring throughout.
Once it boils, turn off the heat and add the vanilla and the unsweetened shredded coconut. Let the mixture cool (you can cool it in the fridge if you are in a hurry).
Once the brownies and the mixture are cool, cut the brownies with a plastic knife and top each one with a scoop of the coconut mixture. If you want you can drizzle some extra melted chocolate on top. Enjoy!