Preheat the oven to 400°F.

Arrange a rack in the center of the oven.

Spray a 9x13-inch pan with nonstick cooking spray. Line the bottom and sides of the pan with parchment paper, then spray the paper with nonstick cooking spray.

In a small saucepan, heat the milk and butter over medium-low heat until the butter melts. Do not let it boil. Alternatively, heat them together in a liquid measuring cup in the microwave. Once melted, remove from heat and set aside to cool slightly while you beat the eggs.

To the bowl of a stand mixer fitted with the whisk attachment, or a large mixing bowl with a hand mixer, add the eggs, sugar, vanilla, and salt. Mix on medium-high speed until pale and fluffy, about 5 minutes. Scrape down the sides and bottom of the bowl with a spatula.

Add the flour and baking powder. Beat on the lowest speed until just combined. Scrape down the sides and bottom of the bowl.

With the mixer running on low speed, slowly stream in the milk and melted butter. Scrape down the sides and bottom of the bowl, then continue mixing until just combined. The batter should be smooth and runny.

Scrape the batter into the prepared pan. Bake until golden brown, and a toothpick inserted into the center of the cake comes out clean, 22 to 24 minutes. While the cake bakes, prepare the topping.

In the same saucepan used to heat the milk, melt the butter over low heat. Add the milk, coconut, brown sugar, and salt, and stir until fully combined and smooth. Do not let it boil. Remove from the heat.

When the cake is done, pour the coconut mixture evenly over the top. Return the cake to the oven and bake until the topping is bubbling, 6 to 8 minutes.

Place the pan on a wire rack. Let the cake cool in the pan for 30 minutes, then unmold the cake onto the rack to cool completely before slicing and serving, 1 to 1 ½ hours.