In a 9-1/2 inch diameter nonstick ovenproof skillet, cook the bacon. Remove to drain on a paper towel and wipe out the skillet.

Heat the oil over a medium flame.

Add the onion and sauté until translucent, about 4 minutes.

Add the potato, garlic, salt and pepper, and sauté over medium-low heat until the potato is tender and golden, about 15 minutes.

Preheat the broiler.

In a medium bowl, whisk the eggs, milk, Parmesan cheese, bacon and basil to blend.

Stir the egg mixture into the potato mixture in the skillet. Cover and cook over medium-low heat until the egg mixture is almost set, but the top is still runny, about 2 minutes.

Place the skillet under the broiler and broil until the top is set and golden brown, about 4 minutes.

Using a rubber spatula, loosen the frittata from the skillet and slide it onto a plate. Cut the frittata into wedges and serve.