Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes.

Meanwhile, place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels. Reserve 2 tablespoons bacon fat in the skillet and discard the rest. Chop bacon when cool enough to handle.

Add 1 tablespoon olive oil and onion to reserved bacon fat in the skillet. Cook over medium-high heat until the onion has softened and turned translucent, about 5 minutes. Add garlic and cook until fragrant, about 1 minute. Pour vermouth into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon, about 1 minute. Mix in chopped bacon.

Drain spaghetti, transfer to a large serving bowl, and mix in remaining 1 tablespoon oil. Add bacon-onion mixture, Parmesan cheese, cream, eggs, and pepper to the hot pasta; stir until spaghetti is well coated and sauce is creamy.