Bring a large pot of generously salted water to a full rolling boil.
As the water heats, finely mince the garlic, slice the bacon into 1/4-inch pieces, grate the Parmigiano Reggiano, and separate the eggs. Place the yolks and whites in different small bowls.
Add the spaghetti to the boiling water and cook until al dente according to the instructions on the package, stirring from time to time.
Before draining the spaghetti, scoop out and reserve 1 cup of the starchy cooking water. Drain the pasta and keep it ready for the final assembly.
Place the bacon pieces in a large skillet or broad pan over medium heat. Cook for approximately 8–10 minutes, or until the bacon becomes crisp and golden.
Using a slotted spoon, transfer the cooked bacon to a paper towel-lined surface. Leave approximately 3–4 tablespoons of the rendered bacon fat in the skillet.
Lower the heat and add the minced garlic to the warm bacon fat. Stir continuously for about 1 minute, until the garlic is aromatic and lightly golden. Avoid allowing it to brown excessively, as burnt garlic can become bitter.
Place the egg yolks in a medium bowl, reserving the whites for another purpose.
Whisk the yolks together with the heavy cream, a generous amount of freshly ground black pepper, and half of the finely grated Parmigiano Reggiano.
While whisking continuously, gradually pour in approximately 1/2 cup of the reserved hot pasta water. Adding the water slowly tempers the yolks and helps prevent them from scrambling.
Continue whisking until the mixture has a smooth, thin, custard-like consistency that can be poured easily.
Transfer the drained spaghetti directly to the skillet containing the garlic and reserved bacon fat. Toss gently until the strands are evenly coated.
Remove the skillet from the heat. Pour the prepared egg-and-cheese mixture over the spaghetti while continuously tossing the pasta with tongs or two forks.
Continue moving the pasta so the residual heat gently cooks the yolks and produces a creamy coating rather than scrambled eggs.
Return the crisp bacon to the skillet and toss until it is distributed throughout the spaghetti.
If the sauce becomes too thick or appears dry, incorporate additional reserved pasta water 1 tablespoon at a time. Toss after each addition until the sauce reaches a silky, fluid consistency.
Immediately divide the finished carbonara among warm serving bowls or plates.
Sprinkle each portion with the remaining grated Parmigiano Reggiano and finish with additional freshly ground black pepper.
Serve at once while the spaghetti is hot and the sauce remains smooth, creamy, and flowing.