Bring a large pot of salted water to a boil and cook the pasta until al dente (tender, but slightly firm to the bite).
Meanwhile, in a large skillet over medium-high heat, heat the olive oil and butter. Add the salami and cook until brown and crisp. Add the garlic and sauté for 1 minute.
In a bowl, whisk the egg yolks. Add the cream, cheese and pepper.
Drain the pasta (saving ½ cup of the starchy pasta water, setting it aside) and add the hot pasta to the skillet. Sauté 30 seconds and toss with the salami. Remove the skillet from the heat and add the egg mixture; toss. If the pasta seems like it needs more moisture, you can add in a little of the starchy pasta water and toss.
Top with additional Parmesan cheese and parsley. Serve immediately.