Preheat oven to 325 degrees. Season beef all over with salt and pepper. Heat 3 tablespoons oil in a large Dutch oven over high heat. Add beef, and brown on all sides. Transfer beef to a rimmed baking sheet. Reduce heat to medium.

Add remaining tablespoon oil to pot. Add onions, and cook, stirring occasionally with a wooden spoon, until edges are browned, 5 to 7 minutes. Add garlic, mushrooms, oregano, and 1 teaspoon salt. Cook, stirring, 3 minutes. Add tomatoes, and crush with spoon. Stir in wine and red-pepper flakes. Return beef to pot, and spoon tomato mixture over top. Cover, and place in oven. Braise until beef is fork-tender, about 4 hours.

Bring a large pot of water to a boil; add 1 tablespoon salt. Add pasta; cook until al dente. Drain, and return to pot.

Remove pot from oven. Using a slotted spoon, transfer beef to a plate. Toss pasta with the sauce; transfer to bowls. Top with pieces of beef, dividing evenly, and garnish with Parmesan.