Clean and separate the cauliflower into florets. Bring a pot of salted water to a boil. Add cauliflower then reduce heat to medium-low, cover, and simmer until fork tender, about 5 minutes. Drain well.
Meanwhile, whisk eggs and milk together in a bowl. Season with salt, pepper, and nutmeg. Add drained cauliflower florets and using a fork, or a masher, press the cauliflower just enough to break down larger pieces. Do not mash it, unless you're really trying to hide it. Fold in the cheese.
Preheat oven to 350 degrees Fahrenheit.
Heat the oil in a 6 or 8-inch cast iron skillet or an ovenproof nonstick skillet over medium heat. Add the cauliflower egg mixture and distribute the filling evenly. Cook until the bottom is just brown, about 5 minutes. Transfer the skillet to the oven and bake until frittata is set on top, about 10 minutes. Remove from the oven and let sit for 5 minutes to finish cooking.
Slice into wedges and serve warm.
~ Free Tip ~Serving suggestion: top with a dollop of sour cream alongside salad greens.