Bring a large pot of well-salted water to a boil and cook the ziti until al dente, then reserve 1/2 cup of the starchy pasta water and drain the pasta.
While the pasta cooks, heat the olive oil and butter in a large skillet over medium-high heat until the butter melts.
Add the Genoa salami strips to the skillet and cook, stirring occasionally, until the salami is browned and crisp.
Add the minced garlic to the skillet and sauté for about 1 minute until fragrant, then remove the skillet from the heat.
In a bowl, whisk together the egg yolks, heavy cream, grated Parmesan, and black pepper until smooth.
Return the skillet to low heat, add the hot drained pasta and sauté for about 30 seconds to combine with the salami.
Remove the skillet from the heat and quickly pour in the egg and cream mixture, tossing constantly so the sauce thickens without scrambling the eggs; add reserved pasta water a little at a time if the sauce needs more moisture.
Stir in the chopped parsley, taste and adjust seasoning, then serve topped with additional Parmesan.