Brush the pizza crust on both sides with 1 tablespoon olive oil. Place crust directly onto the middle rack of the oven and bake for 10 minutes.
While the crust is cooking, break the eggs into a bowl and add the reserved spinach liquid. Whisk them well and season them with salt and pepper. Add the remaining 2 tablespoons olive oil to a 10-inch skillet and heat over medium heat. Add the onions and cook until translucent, about 4 minutes. Add the dry spinach, breaking up the pieces, and heat through, about 2 minutes. Scrape the vegetable mixture into the eggs and beat it well to distribute the spinach evenly. Turn the heat down to low and pour the egg mixture back into the pan. Gently stir the eggs until they are just set and still moist, about 3 to 4 minutes.
Spread the egg mixture evenly onto the baked pizza crust and top with the cheese. Return to the oven until the cheese is melted and lightly browned, about 1 minute. Serve hot.