Beat the eggs in a large bowl. Stir in the salt, pepper, milk, and the filling.
Heat the olive oil over medium-high heat in a heavy nonstick skillet. Use an 8-inch skillet for 2 eggs, a 10-inch skillet for 4 to 8 eggs, and a 12-inch skillet for 10 eggs. Hold your hand above it; it should feel hot. Drop a bit of egg into the pan and if it sizzles and cooks at once, the pan is ready.
Pour in the egg mixture. Swirl the pan to distribute the eggs and filling evenly over the surface. Shake the pan gently, tilting it slightly with one hand while lifting up the edges of the frittata with the spatula in your other hand, to let the eggs run underneath during the first few minutes of cooking.
A 2-egg omelet will be done quickly, with just the tilting of the pan and letting the eggs run underneath until it is no longer or only slightly moist on the top. Once it is set, slip it out of the pan onto a plate. It’s fine to leave the top a little runny (that’s the way they like them in France.)
A larger frittata, one cooked in a 10- or 12-inch pan, must be covered and cooked over low heat. Turn the heat down to low, cover, and cook 5 to 10 minutes, depending on the number of eggs, shaking the pan gently every once in a while. The eggs should be just about set; cook a few minutes longer if they’re not.
Carefully slide from the pan onto a large round platter. Cut into wedges or into smaller bite-size diamonds. Serve hot, warm, at room temperature, or cold.