Preheat oven to 450 degrees F. Grease two 15x10x1-inch baking pans; set aside. For flatbreads, cut thawed dough in half. On a lightly floured surface, roll each half to a 15 x 10-inch rectangle. (If dough becomes difficult to roll, let rest for 5 minutes, then resume rolling.) Press dough into prepared pans, pressing to sides of pans. Prick dough all over with a fork. Bake for 6 to 8 minutes or until very lightly browned.
Meanwhile, for white sauce, in a small saucepan melt the butter over medium heat; stir in flour. Cook and stir for 2 minutes. Slowly whisk in milk. Cook and stir until thickened and bubbly. Add Parmesan cheese; cook for 1 minute.
Spread the white sauce within 1/2 inch of dough edges. Top with mozzarella. Lightly toss asparagus and squash with 1 Tbsp. of the olive oil. Spread asparagus on cheese layer. Bake for 10 minutes, until browned. Cool slightly.
Meanwhile, in a small skillet heat the remaining 2 Tbsp. oil over medium heat. Cook sliced garlic in oil, stirring frequently, until tender and beginning to brown. Remove from heat. Spoon garlic and oil evenly on flatbreads. Sprinkle with green onions. Pass honey.