Preheat oven to 425°F (218ºC) with rack set in middle position.
Bring a large pot of water to a boil. Season generously with salt, then add 1 pound lasagna noodles and cook according to package until al dente. Drain and set aside.
Measure out and set aside 1 cup mozzarella and ½ cup Parmesan and set aside.
In a medium bowl, combine remaining mozzarella and Parmesan, 16 ounces ricotta, ⅔ cup cream, 2 grated garlic cloves, 2 teaspoons oregano, ½ teaspoon red pepper flakes, 2 teaspoons kosher salt and 1 teaspoon black pepper.
Spread 1 cup ragu in bottom of a 9X13-inch baking dish. Top with a layer of noodles (avoid heavy overlapping, though some is inevitable). Top with 1 cup of sauce and dollop a heaping cup of cheese mixture over top; carefully spread into an even layer. Top with another layer of noodles and repeat three more times, ending with noodles (you may have some noodles left over).
Sprinkle reserved 1 cup mozzarella and ½ cup Parmesan evenly over top.
Cover loosely with aluminum foil; place baking dish on a baking sheet and transfer to oven. Bake until sauce is bubbling up around edges, 25–30 minutes. Carefully remove foil and continue baking until lasagna is golden brown on top with crisp edges, 35–45 minutes longer. Let cool slightly before slicing and serving.