Bring a large pot of generously salted water to a boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve 1 cup of the pasta water.

While the pasta is cooking, heat the reserved sun-dried tomato oil in a large skillet over medium heat. Add the minced garlic and chopped sun-dried tomatoes. Cook for 1-2 minutes until the garlic is fragrant, being careful not to burn it.

Pour in the heavy cream and chicken broth. Stir in the dried oregano and red pepper flakes (if using). Bring the sauce to a gentle simmer and cook for 3-4 minutes, stirring occasionally, until it has slightly thickened.

Reduce the heat to low and gradually stir in the grated Parmesan cheese until fully melted and the sauce is smooth. Season with salt and black pepper to taste.

Add the drained pasta to the skillet with the sauce. Toss well to combine, adding a splash of the reserved pasta water as needed to create a silky, smooth sauce that coats the pasta. Stir in the fresh basil, serve immediately, and top with extra Parmesan cheese.