Preheat the oven to 425 degrees.

In a large bowl, whisk the eggs just until the whites and yolks are blended. Whisk in the milk, oregano, Dijon mustard, salt, and pepper. Whisk in the cheeses. Set aside.

Heat the oil in a 12-inch cast iron skillet, or oven-safe skillet over medium-high heat.

Add the spinach and garlic and cook for 2 minutes, until the spinach wilts, stirring frequently to move the uncooked spinach from the top to the hot surface of the pan.

Whisk the egg mixture once more and then pour it over the spinach. Briefly stir with a spatula to combine and distribute the mixture evenly across the pan.

Cook for 1 to 2 minutes, without stirring, until you can see that the frittata is almost cooked through to the surface, leaving about 1/2-inch of uncooked egg mixture on the top. Carefully transfer the frittata to the oven.

Bake for 7 to 8 minutes, until the eggs are puffed and appear cooked, and the center jiggles a little when you gently shake the pan (the center will continue to cook after the pan is removed from the oven). Remove the frittata from the oven and cool on a rack until set (about 5 minutes).

Arrange the ham slices on top of the frittata and top with parsley leaves. Serve warm, room temperature or chilled.

Store leftovers in the refrigerator for up to 3 days. Serve leftover slices chilled, room temperature, or warm from a quick visit to the oven or microwave.