Heat oven to 375°F. Grease a 9×13-inch casserole dish.
Boil noodles in salted water until just shy of al dente. Drain well.
Warm oil in a large skillet over medium-high heat. Brown the beef, breaking it up.
Stir in onion and bell pepper. Cook until softened, about 4 minutes.
Add garlic; cook 30 seconds. Stir in crushed tomatoes, tomato paste, broth, Worcestershire, Italian seasoning, salt, pepper, and red pepper flakes.
Simmer the sauce 8–10 minutes, stirring, until slightly thickened. Adjust seasoning.
Blend cream cheese and sour cream in a bowl until smooth. Season with a pinch of salt and fold in parsley.
Layer half the noodles in the dish. Dollop and spread half the cream mixture over them.
Spoon on half the beef sauce. Sprinkle half the cheddar and half the mozzarella.
Repeat layers with remaining noodles, cream mixture, sauce, and cheeses.
Cover with foil and bake 20 minutes. Uncover and bake 10–15 minutes until bubbling and lightly browned.
Rest 10 minutes before slicing. Garnish with extra parsley and serve warm.