Step 1In a medium heavy-bottom saucepan, bring the cream to a boil. Reduce the heat to a good simmer and cook, stirring frequently, until it is thickened and reduced by about half, about 15 to 20 minutes. Stir in the Gorgonzola and continue to cook, stirring frequently, until the cheese is melted and combined with the cream, 1 to 2 minutes. Remove from heat and reserve in a warm place.
Step 2Bring a large pot of water to boil. Blanch the spinach to bring out the color, then drain and shock in a bowl of ice water. Drain again, pressing out all excess water. Set aside.
Step 3Pound the chicken: Place each chicken breast between two sheets of plastic wrap and pound to a thickness of one-fourth inch without tearing. Season each breast with a pinch of salt and pepper on each side, then dredge in flour to coat.
Step 4In a large saute pan over medium-high heat, heat the oil until hot, then brown the chicken on each side, one piece at a time, 1 to 2 minutes per side. Adjust the heat as needed to keep the chicken from burning, and add oil as needed to keep a thin film on the bottom of the pan. Remove the chicken to a platter to keep warm.
Step 5In the same saute pan, add a little oil if needed to maintain a thin film, then stir in the garlic. Cook over medium-heat just until aromatic. Stir in the spinach, then the sauce. Cook, stirring constantly, for a minute or so to merge the flavors. Remove from heat.
Step 6Heat the broiler and place each chicken breast on an oven-proof plate. Spoon one-fourth of the cream and spinach over each breast, then evenly sprinkle the mozzarella and Parmigiano-Reggiano cheese over each portion.
Step 7Place each plate briefly under the broiler to melt the cheese and brown the sauce slightly. Sprinkle the plates with chopped parsley and serve immediately.