Preheat the oven to 350. Have ready a metal bread loaf pan that measures 9 x 5".
First, make the crust: In a medium bowl, combine the sugar, flour, salt and baking powder. Add the egg yolk, milk and melted butter. Stir until a wet dough forms, and then press this mixture evenly into the bottom of the bread loaf pan.
Next, make the gooey butter filling: In the same bowl you used to make the crust, add all of the filling ingredients. Beat together on low speed until well-blended, about 1 minute. Pour the filling over the crust.
Bake the gooey butter cake for 35-40 minutes. It will be browned on the edges, but slightly jiggly and sunken in the middle. Let it cool COMPLETELY. I store it overnight in the fridge for perfect cuts.