Heat oven to 375°F and set a rack in the center.
Whisk the beaten eggs, milk, salt, black pepper, red pepper flakes, and half the herbs until smooth.
Warm olive oil and butter in a 10-inch oven-safe skillet over medium heat.
Sauté onion until soft, 3–4 minutes. Stir in garlic and cook 30 seconds until fragrant.
Add spinach and cook until wilted. Spread vegetables in an even layer.
Scatter mozzarella and cheddar over the skillet, dot with goat cheese, then pour in the egg mixture.
Cook on the stovetop until edges start to set, 3–4 minutes. Sprinkle Parmesan on top.
Transfer to the oven and bake until just set in the center, 10–12 minutes. Broil 1–2 minutes for extra color if desired.
Rest 5 minutes. Top with remaining herbs and optional tomatoes. Slice and serve warm.