Place a 1-cup ovenproof baking dish on a rimmed baking sheet and place in oven.
Preheat oven to 450 degrees.
While oven is heating, whisk together egg and egg whites, 1 tablespoon cheese, milk, teaspoon salt, and pinch of pepper.
In a small skillet, heat teaspoon oil over medium; add shallot and cook until softened, about 2 minutes.
Add spinach; cook until wilted, about 2 minutes. Season with salt and pepper.
Stir spinach into egg mixture.
Remove heated dish from oven and coat with cooking spray.
Immediately pour in egg mixture and top with 1 tablespoon cheese.
Bake until frittata is puffed up and golden brown, about 15 minutes.
Toss greens with vinegar and 3/4 teaspoon oil; season with salt and pepper.
Serve frittata with salad.