Boil the spaghetti in lots of salted water until just al dente. Don't overcook.
While the spag is cooking, heat the oil in a saucepan. Add the bacon and cook until browned.
Drain the spaghetti and add to the bacon off the heat. Stir in the eggs and cream if using. Season with salt and pepper and stir until the eggs are setting. Add the Parmesan and toss. Serve hot with parsley.