Place one pizza stone on the bottom rack of your oven and another one on the top rack. Preheat the oven for 1 hour at 500 degrees F or on broil. This will help the stones absorb some heat and give you an extra 50 to 100 degrees.
Mix the ricotta, 1/4 cup of the Parmigiano and the whipping cream in a medium bowl.
Sprinkle a little flour or semolina on a wooden pizza peel. Stretch the dough into a 12-to-14-inch circular shape and place it on the pizza peel. Brush the crust with the oil.
Spread the ricotta mixture in an even layer over the pizza. (If there is a little leftover, you can use for a dip for the crusts!) Sprinkle the shredded mozzarella over the ricotta, and then lay slices of the fresh mozzarella on top. Top the pizza with 1 teaspoon pepper and 2 tablespoons of the Parmigiano.
Slide the pizza onto the bottom pizza stone and let cook until the crust is golden brown and the cheese is brown and bubbling, 10 to 15 minutes.
Top the pizza with remaining 2 tablespoons Parmigiano, 1 teaspoon pepper and season with salt. Slice and serve with any remaining ricotta mixture.