Bring a pot of salted water to a boil and cook the pasta until al dente, following the package directions. The noodles should be tender with a firm center, since they will finish coating in the hot sauce.

While the pasta nears doneness, melt the butter in a skillet over medium-high heat and stir in the flour for about 2 minutes. Keep stirring until the roux looks pale and smooth with no dry flour visible.

Add the minced garlic and chicken broth, then let the mixture simmer for about a minute. The skillet should smell warmly garlicky as the broth loosens the roux into a glossy base.

Whisk in the heavy cream and cook for a few more minutes, stirring occasionally, until the sauce thickens to your liking. Look for small, lazy bubbles rather than a fast boil, and stop when the sauce lightly coats a spoon.

Take the skillet off the strongest heat, stir in the parmesan, and season with salt and pepper as needed. The cheese should melt into a smooth sauce without clumps or oily streaks.

Drain the pasta and toss it thoroughly with the sauce, adding a little reserved pasta water if needed. Serve immediately with parsley and extra parmesan if desired, while the sauce is still glossy and fluid.