Bring a large pot of generously salted water to a boil. Add the pasta and cook according to package directions until al dente. Reserve 1/2 cup of the starchy cooking water before draining.
While the pasta cooks, heat the olive oil in a large skillet over medium-low heat. Add the sliced garlic and red pepper flakes. Cook gently for 3-4 minutes, stirring frequently, until the garlic is golden but not browned—it should smell fragrant and look like pale gold coins.
Pour in the heavy cream and white wine (or broth). Stir and let it come to a gentle simmer. Cook for 2-3 minutes until slightly thickened—about half the original volume. The sauce should coat the back of a spoon lightly.
Add the butter and grated Parmesan, whisking constantly until melted and smooth. Taste and adjust seasoning with salt and pepper. If the sauce is too thick, add some reserved pasta water a tablespoon at a time.
When the pasta is ready, transfer it directly to the skillet with the sauce using tongs—don't drain it completely yet. Add a splash of the reserved cooking water and toss everything together over low heat for 1-2 minutes until the sauce clings to every strand.
Remove from heat. Taste one more time before serving—it should be rich but not heavy. Serve immediately with torn basil leaves, extra Parmesan on top, and a drizzle of olive oil if desired.
