Heat water for pasta in large pot, salt it and add pasta for 3 minutes.
While water boils, heat a large skillet with extra-virgin olive oil, 3 turns of the pan, over medium-high heat. Add pancetta and brown, 3 to 4 minutes. Add garlic and red pepper flakes.
Drain pasta, add to pan and toss. Stir in Parmigiano-Reggiano and season with salt and pepper. Beat eggs with cream and pour over top of pasta. Let eggs begin to set up, about 1 minute, and pat pasta into even layer to make the pizza pie crust. Place in oven and cook 5 to 6 minutes.
Mix together the ricotta and parsley. Remove pie from oven and smooth the ricotta over the top. Scatter with the provolone or mozzarella and return to oven. Bake 8 minutes more until cheese is melted and golden at edges. Cut into wedges and serve.