Bring a large pot of salted water to a rolling boil and cook the ziti until al dente according to package directions.
While the pasta cooks, heat the olive oil and butter in a large skillet over medium-high heat.
Add the Genoa salami strips to the skillet and cook until browned and crisp, about 3–5 minutes.
Add the minced garlic to the skillet and sauté for about 1 minute until fragrant; remove from heat if the garlic begins to brown too quickly.
In a bowl, whisk together the egg yolks, heavy cream (or half-and-half), grated Parmesan, and freshly ground black pepper until combined.
Reserve 1/2 cup of the hot pasta cooking water, then drain the pasta and immediately add the hot pasta to the skillet with the salami; sauté and toss for about 30 seconds to combine.
Remove the skillet from the heat and quickly add the egg-cream mixture, tossing constantly to create a creamy sauce; add a splash of reserved pasta water as needed to loosen the sauce.
Transfer to plates, top with additional Parmesan and the chopped parsley, and serve immediately.