Remove the casing from the sausages and cut them into 1-inch pieces.
Place a large skillet with the oil over low heat and when the oil is warm, add the sausages and garlic and sauté until completely cooked, for about 10 minutes. Discard the garlic.
Meanwhile bring a large pot of cold water to a boil, and when the water reaches a boil, add coarse salt to taste, then the pasta and cook until al dente for 9 to 12 minutes, depending on the brand.
Meanwhile mix the eggs with the cheese in a small crockery or glass bowl.
Raise the heat on the sausages and season with salt and pepper. Keep stirring to be sure the sausages do not stick to skillet.
When the pasta is ready, drain it and transfer to skillet over high heat, sprinkle with more pepper, and sauté for a few seconds, mixing very well with two forks.
Remove skillet from the heat, pour the mixed eggs over the pasta, sprinkle with parsley, mix again thoroughly, and serve directly from the pan.