Heat oven to 425°F. Unroll dough with oven-safe parchment paper and place onto a large cookie sheet (dough bakes on paper). Brush with olive oil. Bake 7 minutes. Remove from oven and set aside.
Meanwhile, melt butter in a medium nonstick skillet over medium heat. Add onion and salt; cook 10-15 minutes, stirring occasionally, until onion softens and begins to brown. Add mushrooms; cook an additional 5-7 minutes or until softened and also beginning to brown. Stir in garlic; remove from heat.
Spread mushroom mixture evenly over dough. Top with spinach, mozzarella cheese and Parmesan cheese.
Bake 7 to 11 minutes longer or until cheese is melted and crust is golden brown. Sprinkle with thyme.