Cook the pasta in a pot of boiling water according to the package directions. Drain, reserving some of the cooking water.
Set a large pan with straight sides over medium-high heat and add the olive oil and sausage. Cook, breaking up the sausage, until brown, about 5 minutes, then season with salt and a few hefty grinds of coarse black pepper -- it's all about the pepper!
In a small bowl, whisk together the Parmesan cheese and eggs.
Add the drained pasta to the pan and swirl until it's mostly coated with the fat of the sausage. Remove the pan from the heat and add a spoonful or so of the pasta water along with the egg and cheese mixture. Toss rapidly to coat the pasta with the eggs and cheese. Continue to toss until the water evaporates a bit and creates a bit of a sauce. Add the parsley and toss again. Serve immediately.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.