Step 1

Preheat the oven to 425 degrees F and position an oven rack in the lower third of the oven.

Step 2

For the pizza crust, combine the water, yeast, sugar, salt and oil. Add the flour until a soft dough forms and pulls away from the sides of the bowl (this can be done by hand or in the bowl of an electric stand mixer). You may not need to add the full amount of flour - or, you may need to add more than the 4 cups, it will depend on many factors. The goal is a soft, smooth dough so judge by texture and feel and not by exact flour amounts. Knead for 2-3 minutes. Cover the dough lightly and let it rest while preparing the other components.

Step 3

For the cinnamon streusel topping, stir together the brown sugar, flour and cinnamon. Add the soft butter and mix with a pastry blender or your fingers until the mixture is crumbly and the butter is well-distributed.

Step 4

For the apple mixture, heat the butter in a 10- or 12-inch skillet until melted. Add the chopped apples, brown sugar and cinnamon, and cook, stirring often, until the apples are tender (but not mushy) and the mixture is thick and bubbly, 4-5 minutes.

Step 5

Press the dough into a 16-inch pizza pan (or it can be stretched into a rectangular baking sheet if that is all you have). The dough should be about 1/4-inch thick. Scoop spoonfuls of the apple mixture over the dough. It won't cover the dough completely, just distribute the apples as evenly as possible. Sprinkle the cinnamon streusel over the top of the apples. Let the pizza rest for about 10 minutes to allow the dough to puff slightly.

Step 6

Bake the pizza for 12-15 minutes, until the edges are browned and the pizza topping is hot and bubbly. While the pizza bakes, prepare the glaze by heating the butter and milk in a medium saucepan until melted. Add the vanilla. Mix in the powdered sugar gradually, whisking to combine until the glaze is smooth.

Step 7

Let the pizza rest for 10 minutes before drizzling the glaze over the top (you can also drizzle glaze on each individual piece as it is served). Serve the pizza warm. Leftovers can be refrigerated and reheated briefly in the microwave.