Bring a large pot of salted water to a rolling boil. Cook the pasta until al-dente, about 6-8 minutes, or to the desired tenderness. Reserve ½ cup of pasta water, then drain
While the pasta cooks, melt the butter in a skillet over medium heat until foamy but not browned.
Add the garlic and onion and sauté for 30 seconds, just until fragrant. Do not let it brown.
Pour in the cream and oregano, stir to combine. Add pasta water accordingly. Reduce the heat to medium-low and simmer gently for 3–5 minutes, until the sauce begins to thicken slightly.
In a large skillet, cook sausage until golden brown.
Add the pasta to the sausage combination, add the sauce mixture, and toss to coat evenly in the sauce.
Stir in the grated cheese. Season with salt and pepper to taste and cook for another 1-2 minute, until the cheese is melted and the sauce coats the pasta.
Remove from heat and drizzle in the extra-virgin olive oil.
Garnish as desired and serve immediately.