Cook the pasta according to package instructions. Reserve 1/2 cup of pasta water before draining.
In a large skillet, heat olive oil over medium heat. Add garlic and red pepper flakes, sautéing for about 1 minute.
Pour in the crushed tomatoes, oregano, and basil. Simmer for 5 minutes, stirring occasionally.
Reduce the heat to low, then stir in the heavy cream and Parmesan cheese. Season with salt and black pepper.
Add the cooked pasta to the sauce, tossing to coat evenly. If needed, add reserved pasta water to adjust consistency.
Serve warm, garnished with fresh basil and extra Parmesan cheese.