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For the cake:
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Preheat oven to 375 F.
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Put the warm milk in a small bowl. Dissolve yeast in the warm milk, then set aside.
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In the bowl of your stand mixer, cream butter, sugar and salt. Add egg and beat one minute until well blended. Add flour and mix to combine. Then add the milk-yeast mixture and vanilla to the batter. Mix for three minutes with the dough hook or by hand. If mixing by hand, turn out onto a floured board and knead for one minute. Otherwise, this can be kneaded using the dough hook with your stand mixer.
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Place dough in a lightly greased bowl, cover with a towel and set in a warm place to rise for one hour or until doubled. Meanwhile, prepare topping and then set it aside.
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For the topping:
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In a medium sized bowl, cream butter. In another bowl, stir together flour and sugar. Gradually beat the sugar mixture into the butter. Add eggs, one at a time, beating well after each addition. Add milk, one tablespoon at a time, just until the mixture reaches a spreadable consistency. It should still be thick!
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Putting it together:
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Pat dough into a 9x13 pan, bringing dough halfway up sides of pan to hold the filling. Prick dough all over with a fork. Pour topping over dough, spreading evenly. Let cake stand 20 minutes before baking in the preheated oven for 30 minutes. Do not over-bake! (I cannot overstate this). Topping should be crusty, but gooey. It should jiggle slightly when shaken. Allow cake to cool before cutting.
