Preheat oven to 375°F; whisk eggs, milk, salt, and pepper in a large bowl and set aside.
Heat oil in a 10-inch oven-safe skillet over medium; cook onion and pepper about 5 minutes until softened.
Add spinach and tomatoes; cook another 2-3 minutes until spinach wilts.
Pour eggs evenly over vegetables; sprinkle with cheese and stir gently to distribute.
Cook on stovetop 3-4 minutes without stirring until edges begin setting.
Bake skillet 15-18 minutes until center sets and top is lightly golden; cool 5 minutes before cutting into wedges.