Brown the beef. Heat 1 tablespoon olive oil in a large, deep skillet over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until no longer pink, about 5-7 minutes. Season with salt and pepper. Transfer to a plate lined with paper towels to drain excess fat.
Sauté the vegetables. In the same skillet, add the remaining tablespoon of olive oil. Add the onions and cook until softened, about 3 minutes. Add the mushrooms and cook until they release their moisture and begin to brown, about 5-7 minutes. (Don't rush this step—those browned mushrooms are flavor bombs!)
Build the flavor base. Add the garlic, Italian seasoning, and red pepper flakes (if using). Cook for 30 seconds until fragrant. Stir in the tomato paste and cook for another minute to caramelize slightly.
Deglaze the pan. Pour in the red wine (or broth) and scrape up any browned bits from the bottom of the pan with a wooden spoon. Let the liquid reduce by half, about 1-2 minutes.
Add liquids and pasta. Return the cooked beef to the skillet. Add the diced tomatoes with their juice and beef broth. Stir in the dry pasta. Bring to a boil, then reduce heat to medium-low, cover, and simmer for about 10-12 minutes until the pasta is al dente, stirring occasionally to prevent sticking.
Finish with creaminess. Once the pasta is tender, stir in the cream and Parmesan cheese. If adding spinach or frozen peas, fold them in now and let them heat through for 1-2 minutes.
Final touches. Remove from heat and let stand for 5 minutes to allow the sauce to thicken slightly. Taste and adjust seasoning if needed. Garnish with chopped parsley and additional Parmesan cheese before serving.