1. Let pizza dough come to room temperature, then preheat the oven to 350° Fahrenheit (176° Celsius).
2. On a nonstick floured surface, roll out the dough into a rectangle under 1/8th of an inch thick.
3. Spread softened butter or oil evenly over the rectangle.
4. In a medium bowl, stir the strawberries, sugar, cornstarch, and optional cinnamon until well mixed.
5. Spread this strawberry filling over the top of the pizza dough.
6. Tightly roll the dough into a long log shape, then use a knife or pizza cutter to slice thin strips. Do not worry if some of the strawberry liquid seeps out.
7. Arrange the rolls in an 8 inch pan. Bake 35 minutes on the center rack of the oven, until dough is fully cooked and lightly golden and filling is bubbly.
8. Bring the cream cheese to room temperature, then use a stand mixer or hand beaters to whip cream cheese, vanilla, and about half a cup of powdered sugar until fluffy.
9. Slowly beat in the remaining powdered sugar. If glaze is too thick, add a tablespoon of milk or more as desired to thin it out.
10. Frost the strawberry sweet rolls while they are still warm, so the icing melts into the top.