How to Make It
In a large heavy skillet, cook the bacon over medium heat until browned, about 8 minutes. Stir in the garlic and chile and cook until the garlic is golden, about 2 minutes. Remove the skillet from the heat and let cool to warm.
In a large pot of boiling salted water, cook the spaghetti until al dente, then drain. Re-serve 1/2 cup of the pasta cooking water, then drain the pasta.
In a bowl, whisk together 4 of the eggs and the cheese, then whisk the egg mixture into the bacon mixture in the skillet. Toss the pasta and the reserved pasta cooking water with the egg and bacon mixture. Season with salt and pepper to taste, then transfer to serving plates. Clean the skillet.
In the skillet, heat the oil over medium high heat until hot. Cook the remaining eggs (1 per serving) in the skillet to desired doneness, about 4 minutes for runny yolks. Top the spaghetti carbonara with the fried eggs and serve.