Combine the instant yeast, sugar, hot water, and warm milk in a mixing bowl. Stir until the yeast dissolves.
Add the salt and oil. Stir in 1 cup of the flour and mix well.
Gradually add enough of the remaining flour to form a soft dough. Knead the dough a few times on a lightly floured surface.
Return the dough to the bowl, cover it, and let it rest for 15 minutes.
Lightly grease a cookie sheet or pizza pan. Roll or press the dough into a 12-inch circle.
For the cinnamon crumb topping, combine the flour, brown sugar, granulated sugar, cinnamon, and softened butter in a small bowl. Mix until crumbly.
Sprinkle the cinnamon crumb mixture evenly over the pizza crust.
Bake at 375°F for 15 to 20 minutes, or until the crust is lightly browned.
Whisk together the powdered sugar, vanilla, and milk until smooth. Add only enough milk to reach a drizzle consistency.
Drizzle the vanilla icing over the baked Cinnamon Dessert Pizza. Slice and serve warm.