Position a rack in the lower third of the oven and preheat the oven to 425°F (220°C).

For the crust, whisk the warm water, instant yeast, granulated sugar, salt, and vegetable oil together in a large bowl. Gradually mix in 3 to 4 cups of flour, working by hand or with a stand mixer, until the dough is soft and pulls away from the sides. Do not rely on an exact flour amount; the dough should feel smooth and slightly elastic. Knead for 2 to 3 minutes, cover the bowl lightly, and let the dough rest while you make the toppings.

For the streusel, stir the brown sugar, flour, and cinnamon together in a small bowl. Drop in the softened butter and use a pastry blender or your fingertips to rub it in until the mixture is crumbly and evenly combined.

For the apple filling, melt 1 tablespoon of butter in a 10 or 12 inch skillet over medium heat. Add the chopped apples, brown sugar, and cinnamon, and cook, stirring often, for 4 to 5 minutes, until the apples are just soft and the juices are thick and bubbling. Remove from the heat.

Press or stretch the dough into a lightly greased 16 inch pizza pan, shaping it to about 1/4 inch thick. Drop spoonfuls of the apple filling evenly over the dough; the filling will not cover every inch. Sprinkle the streusel over the apples, then let the pizza rest for about 10 minutes so the dough puffs.

Bake the pizza for 12 to 15 minutes, until the edges are golden brown and the filling is hot and bubbly. While it bakes, prepare the glaze by heating the butter and milk in a small saucepan until the butter melts. Remove from the heat, stir in the vanilla, then gradually whisk in the powdered sugar until the glaze is smooth.

Let the pizza cool for 10 minutes before drizzling the glaze over the top, or drizzle each slice as you serve. Serve warm. Store leftovers in the refrigerator and reheat briefly in the microwave.