1 1/2 pounds boneless, skinless chicken breasts
Kosher or coarse salt and freshly ground black pepper, to taste
2 tablespoons unsalted butter
1 teaspoon minced garlic
4 cups chicken broth, preferably low-sodium
1 pound penne rigate or ziti pasta (see Recipe Note)
1 1/2 cups heavy (whipping) cream or half-and-half, warmed
1 cup freshly grated Parmesan, plus more for serving
1/4 cup chopped fresh flat-leaf parsley (optional)