For the pasta, bring a large pot of salted water to a boil (at least 4 quarts of water and 2 tablespoons of salt). For the eggs, fill a wide saucepan with 2 inches of salted water and bring to a boil. Add the vinegar to the saucepan for the eggs.

In a large (12-inch) skillet over medium-high heat, cook the bacon until browned. Transfer to plate.

Add the garlic and the tomatoes, and cook, stirring often, for 2 minutes, or just until the garlic turns pale golden and the tomatoes soften slightly. Remove the pan from the heat.

Add the spaghetti to the large pot of boiling water, and cook for 8 to 9 minutes, or until al dente. Remove 1 cup of the pasta water with a measuring cup.

Line a tray or plate with a paper towel. Adjust the heat under the saucepan so that the poaching water barely simmers.

Crack 1 egg into a small bowl or cup and, holding the rim as close to the surface of the water as possible, drop the egg into the water.

Rapidly repeat with the remaining eggs.

Drag a wooden spoon around the edge of the pot to stir the water and gently release the eggs from the bottom.

After 2 minutes, lift 1 egg from the water with a slotted spoon and test for doneness by pressing on the egg. The white should feel firm and the yolk should still be soft. Return to the water if necessary to complete the cooking. With a slotted spoon, transfer the eggs to the paper towel lined plate to drain the water.

Set the skillet with the garlic and tomatoes back over low heat. With tongs, add the cooked spaghetti. Add the cooked bacon, Parmesan, basil, salt, and pepper and toss together. If the spaghetti looks dry, add some of the reserved pasta water a few tablespoons at a time.

Divide the spaghetti among 4 plates or shallow bowls and top each with a poached egg. Drizzle with olive oil and sprinkle with freshly ground pepper, if you like.