In a large bowl, whisk together the eggs, cream, salt and pepper. Set aside.
In a 10″ skillet, melt the butter over medium-high heat. Add the vegetables and cook, stirring until the vegetables are soft and lightly browned, 2 to 3 minutes.
Add the pancetta, garlic and 1/2 tbs parsley, and cook until the garlic is fragrant, 20 seconds to 1 minute. Place vegetables in a bowl and set aside.
Pour the egg mixture in the skillet on medium-high heat for 30 to 60 seconds. Add the pancetta/vegetable mixture. Bake 20 to 25 minutes at 350 degrees until the eggs are firm. Sprinkle the cheese over the top to melt.
Remove from oven and slide frittata onto a large serving platter. Garnish with the remaining 1/2 tbs parsley, chopped green onions and basil oil (optional). Serve immediately.