Cook pasta according to packaging; drain and set aside.
Meanwhile, in a large saucepan, heat oil over medium heat. Add onion and cook 4 minutes, until softened. Add garlic, thyme, cayenne, pepper and basil; cook on low for 5 minutes, stirring occasionally.
Add hot sauce, Worcestershire sauce, tomato, sugar, and broth. Bring to a boil, reduce to a simmer and cook 30 minutes, until liquid is reduced by half. Season with salt, if desired.
In a separate small skillet, heat butter over medium heat. Add shrimp and cook 2 minutes, until light pink. Add to pasta sauce and cook 5 minutes, stirring to combine thoroughly. Add the cooked pasta and toss well with the grated cheese. Serve topped with fresh grated cheese and green onions.