Feel free to substitute frozen baby peas if you have trouble finding fresh ones. Slideshow: More Pasta Recipes
In a large heavy skillet, cook the bacon over medium heat until browned and crisp, 6 to 8 minutes. Transfer the bacon to paper towels to drain, reserving the fat in the skillet. Remove the skillet from the heat and let cool to warm.
In a medium bowl, whisk together the eggs, yolks, and 3/4 cup cheese. Whisk the egg mixture into the cooled fat in the skillet.
In a large pot of boiling salted water, cook the spaghetti until al dente. 3 minutes before the pasta is finished cooking, stir the peas into the pot with the pasta. Reserve 1/2 cup of the pasta cooking water, then drain the pasta and peas.
Immediately add the hot pasta to the egg mixture in the skillet, turning with tongs to coat the spaghetti with the egg sauce. Stir in some of the re-served pasta cooking water if you prefer a looser consistency. Season the pasta with salt and pepper to taste, then serve, topped with the crumbled reserved bacon and additional cheese.