Combine 1 cup milk, 1 tablespoon butter and 1 teaspoon vanilla in a small saucepan and heat to almost boiling. Remove from heat and set aside.
Beat the eggs and sugar in mixer until it is thick, about 2 minutes. Stir in the flour mixture until it is just smooth. Add the hot milk mixture and stir until well-combined.
Pour the batter into the prepared baking dish and bake for 30 minutes or until toothpick inserted in the center comes out clean, about 30 minutes. Cool on a rack for 10 minutes while you make the frosting.
Stir the melted butter, brown sugar, 1/4 cup milk and coconut together. Spread over the warm cake, making sure you cover it all the way to the edges.
Place under the broiler until golden, watching it the entire time so it doesn’t get too dark, about 2 minutes or so.
Remove and cool, and then cut into squares and enjoy with a friend!