Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain.
Meanwhile, heat oil in a skillet over medium heat. Add onion; cook until soft and translucent, about 5 minutes. Add garlic; cook until fragrant, about 30 seconds. Stir in mushrooms and bell pepper; cook until mushrooms lightly browned and bell pepper softened, 3 to 5 minutes. Add shrimp, white wine, and oregano; cook until shrimp begin to turn pink, 3 to 5 minutes.
Stir in cream and butter; simmer, stirring constantly, for 8 minutes. Add cooked spaghetti; stir to combine. Turn off heat. If sauce is too thin, thicken with flour. Season with salt and black pepper; sprinkle with Parmesan cheese and basil.
