To make the cake layer: Grease a 13 × 9-inch pan. In a small bowl, mix together the warm milk and yeast. Let stand for 5 to 10 minutes, until the mixture begins to foam slightly. Set aside.
Whisk together the flour and salt in a medium bowl and set aside. In a separate bowl, use an electric mixer to cream the butter and granulated sugar until smooth. Add the egg and vanilla and beat until light and fluffy, 4 to 5 minutes. Add the flour to the egg mixture, combining by hand and alternating with the milk. Stir until just smooth. This will be a dense, slightly elastic dough.
Turn the dough out into the prepared pan. Press the dough evenly into the pan to fill it. Cover the pan loosely with a dish towel or plastic wrap and place in a warm spot to rise, about 3 hours. The cake should double in size and look bubbly and irregular.
To make the topping: Use an electric mixer to cream the butter and sugar until smooth. Add the eggs and vanilla and beat until combined. Whisk together the flour and salt, then gradually add it to the butter mixture, alternating with the milk; the mixture should be spreadable but not too runny. Set aside.
Heat the oven to 350°F. Use a fork to prick a few holes into the dough so that it doesn’t bubble too much. Spoon the topping in generous dollops over the surface of the cake, then gently connect the dollops, spreading the topping evenly over the dough. Bake until the cake is a light golden brown on top, 35 to 45 minutes. The cake will still be liquid in the center. Serve slightly warm or cool.
My books include the bestselling How to Cook Everything and Vegan Before 6 P.M. (VB6), where I provide all the necessary tools for making the switch to a Flexitarian diet with lists for stocking the pantry, strategies for eating away from home in a variety of situations, pointers for making cooking on a daily basis both convenient and enjoyable, and a complete 28-day eating plan showing VB6 in action.