In a large bowl, whisk together the eggs and cream. Stir in the cheese, pasta, 2 tablespoons of the thyme, parsley, lemon zest, salt, and pepper.
In a 10-inch nonstick skillet, heat the oil over medium heat. Pour the egg mixture into the pan and cook for 7 to 8 minutes until the edges begin to brown. Remove the pan from the heat. Using a spatula, slide the frittata onto a dinner plate. Carefully invert the frittata back into the skillet and continue to cook until firm, 5 to 6 minutes
Garnish with the remaining thyme. Cut into wedges and serve warm or at room temperature.