Preheat the oven to 425. Gently beat the eggs until all yolks are broken and just
combined. Add the whole milk and all spices; set aside. In an oven-safe skillet, heat the oil over medium. Add the shallot, stirring and cooking until fragrant and translucent. Add the pepper and mushrooms, stirring and cooking until softened. Add the greens (may do this in batches) until cooked down and wilted. Whisk the egg mixture once more, then pour into the pan and gently stir to combine all ingredients. Add half of the cheese. Allow to cook undisturbed until the outside edge turns lighter in color, approx. 1-2 minutes.
CarefuIly transfer the frittata to the oven and bake for 7-14 minutes (keep an eye on it!) until the eggs are puffed and appear cooked and the middle jiggles just slightly. Sprinkle with remaining cheese in the final minutes of cooking. Remove from oven and place on a cooling rack. Garnish with herbs, cut with a sharp knife and serve.