One of my favorite pastas to make.
Sauté bacon in a skillet until golden brown and crisp. Remove with a slotted spoon and drain well on a paper towel-covered plate.
Bring 6 quarts of water to a boil in a large pot. Add a pinch of salt and then drop in spaghetti. Cook until al dente (follow package directions), stirring occasionally to prevent strands from sticking together. Reserve a cup of pasta water.
Meanwhile, beat the eggs thoroughly in a large serving bowl. Whisk in a little of the hot pasta water to temper eggs.
When the pasta is ready, drain it in a colander (be sure to reserve a cup of pasta water). Then immediately pour drained hot spaghetti into the bowl of eggs and toss quickly to cook eggs. Add pasta water to thin sauce as necessary.
Add cheese, bacon and basil to bowl and toss again. Top with freshly ground black pepper and serve immediately.
Adapted from "The Silver Palate Cookbook" by Julee Rosso & Sheila Lukins.