Place a large pot or deep skillet over medium heat. Melt the butter until it starts to bubble, then add the minced garlic. Sauté the garlic for about 1 minute until it becomes fragrant, but be careful not to let it brown or burn, as this will make the sauce bitter.

Pour the chicken broth and heavy cream into the pot with the garlic butter. Stir well and bring the liquid to a gentle simmer. Add the dry pasta to the pot. Use tongs to submerge the noodles as they soften. Cook for about 10 to 12 minutes, stirring frequently to ensure the pasta does not stick to the bottom and that it absorbs the liquid evenly.

Once the pasta is al dente and the liquid has reduced into a thick sauce, turn off the heat. Stir in the freshly grated Parmesan cheese until it is fully melted and the sauce is silky. Season with salt and pepper to taste. Garnish with fresh parsley and serve immediately while hot.