Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente, approximately 12 minutes. Drain and rinse briefly under cool running water to halt further cooking. Set aside.

In a large skillet over medium-high heat, cook the bacon until it becomes crisp, about 10 minutes. Transfer the cooked slices to a paper towel-lined plate. Discard most of the bacon grease, reserving approximately 2 tablespoons in the skillet. Chop the bacon into small pieces once cooled slightly.

To the same skillet with the reserved bacon fat, add 1 tablespoon of olive oil and the chopped onion. Sauté over medium heat until the onion becomes soft and translucent, about 5 minutes. Add the minced garlic and cook for an additional minute, or until fragrant.

Pour in the dry vermouth and allow it to come to a gentle boil. Use a wooden spoon to scrape up the browned bits at the bottom of the skillet. Stir in the chopped bacon and mix until evenly combined. Remove from heat.

In a large serving bowl, place the cooked spaghetti and drizzle with the remaining tablespoon of olive oil. Add the bacon and onion mixture, then immediately add the beaten eggs, Parmesan cheese, heavy cream, and black pepper. Toss vigorously to ensure the eggs cook gently and the ingredients combine into a smooth, creamy sauce. Serve immediately.