Bring a large pot of lightly salted water to a boil. Add the angel hair pasta and cook for 8 to 10 minutes or until al dente. Once done, set aside 1/2 cup of the pasta water, then drain the pasta in a colander in the sink. Keep warm.
While the pasta is cooking, melt the butter in a saucepan over medium heat. Stir in the onion and cook for 3 minutes, then stir in the garlic and continue cooking until the onion has softened and turned translucent, 1 to 2 minutes more.
Pour in the cream, and stir in the Parmesan cheese, basil, salt and pepper. Bring to a simmer, then reduce heat to medium-low and simmer for 2 minutes. Dilute with the reserved pasta water if the sauce is too thick for your taste. Pour the sauce over the angel hair pasta to serve.