In a large Dutch oven, heat oil over medium heat. Add onion and cook about 3 minutes. Stir in garlic and cook 30 seconds. Stir in meat, salt and pepper. Cook about 4 minutes, breaking meat into small pieces while it browns.
Stir in cream, bring to simmer and cook until liquid evaporates and only fat remains. Stir in puree, diced tomatoes and oregano. Bring to simmer and cook about 3 minutes. Season with salt and pepper to taste.
In a medium bowl, stir together ricotta, egg, 1 cup Parmigiano, basil, egg and 1/2 tsp salt and pepper until combined. Set aside.
Prepare a deep 9x13-inch baking dish or two 9-inch square pans. Preheat oven to 400 degrees.
Spread 1 cup of sauce over bottom of baking dish. Place 3 noodles in single layer atop sauce. spread 1/3 cup ricotta mixture over noodles, then sprinkle with 1 cup mozzarella. Spoon a cup of sauce of cheeses. Repeat layers with remaining noodles, ricotta, mozzarella and sauce with a layer of mozzarella and 1/2 cup Parmigiano on top.
Spray a piece of foil with cooking spray and cover dish. Bake for 20 minutes. Remove foil and bake for 30 minutes longer. Remove from oven and let cool 10 minutes before slicing into squares.