How to Make It
Heat oven to 425° F. Brush 2 large baking sheets with oil. On a lightly floured surface, shape the dough into four 8-inch rounds and place on the baking sheets.
Dividing evenly, top the rounds with the marinara sauce, mozzarella, mushrooms, and onion; season with ¼ teaspoon each salt and pepper. Bake, rotating the baking sheets halfway through, just until the crust begins to brown, 18 to 20 minutes.
Carefully crack an egg on top of each pizza and return to oven. Bake, rotating the baking sheets halfway through, until the egg whites are set, 5 to 7 minutes.
In a large bowl, toss the greens with the vinegar, the 2 tablespoons of oil, and ¼ teaspoon each salt and pepper. Serve with the pizzas.