Put the pasta to boil according to package directions. Leave them al dente and do not overcook them. Drain the cooked pasta. Heat oil in a Teflon pan with a wide bottom and saute the chopped onion.
Add the bacon and fry it until reddened. Gradually pour in the cream and reduce the heat to keep the sauce from boiling. While stirring, add the first two egg yolks and stir, then add 1/5 cup (60 ml) of the water used to cook the pasta.
Sprinkle with grated parmesan. Add salt and pepper to taste. Once the sauce is slightly thickened, turn off the heat and add the cooked and drained spaghetti. Stir well and distribute into plates. Serve the spaghetti carbonara, sprinkled with a little basil.