Preheat the broiler. Heat 1 tablespoon of the olive oil in large oven-proof nonstick skillet over medium heat. Add the shallots, red pepper, oregano, thyme, red pepper flakes and a pinch each of salt and pepper. Cook, stirring occasionally, until the shallots and peppers are soft, 7 minutes. Transfer to a small bowl and cool; don't wash the skillet.
Beat the eggs, heavy cream, 1/4 teaspoon salt and 1/4 teaspoon pepper in a large bowl. Stir in the shallot mixture. Heat the remaining 3 tablespoons olive oil in the nonstick skillet over medium heat. Pour in the egg mixture and spread the vegetables evenly throughout the pan. As the eggs set, lift the edges to allow the liquid egg mixture to run underneath. Cook until the eggs are mostly set but the center is still a little runny, 10 to 15 minutes.
Sprinkle the Parmesan and goat cheese over the top and broil until the top is golden brown, about 2 minutes. Carefully remove the skillet from broiler and loosen the edges of frittata. Cool for 10 minutes in the skillet, then serve slices from the pan or slide onto a serving platter, slice and serve.