How to Make It
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, 3/4 cup cheese, and sun dried tomatoes. 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. Reserve 1/2 cup of the pasta cooking water, then drain the pasta. 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 reserved pasta cooking water if you prefer a looser consistency.
Season the pasta with salt and pepper to taste, then serve, topped with the goat cheese, crumbled reserved bacon, and additional parmesan cheese.