Heat oven to 350° F.
Melt butter in a 10-inch oven-proof nonstick skillet over medium-high heat. Add shallots and cook for 4 minutes, stirring occasionally. Add capicola and cook for 1 minute.
Whisk together eggs, milk, pepper and nutmeg; stir in 4 oz of the cheese and pour into skillet. Cook for 5 minutes, stirring once after 2 minutes.
Place skillet in oven and bake at 350° F for 5 minutes. Scatter remaining 2 oz cheese on top and bake an additional 5 minutes until frittata is set.
To serve, gently slide frittata onto a serving plate and garnish with basil, if desired.