| 1 1/2 cups heavy cream | |
| 4 tablespoons (1/2 stick) unsalted butter | |
| 2 pinches freshly grated nutmeg | |
| 1 1/2 cups grated Parmesan | |
| Kosher salt | |
| 18 ounces frozen cheese tortellini | |
| 2 boneless, skinless chicken breasts, cut into 1-inch pieces (about 1 1/4 pounds) | |
| 1/4 cup chopped fresh flat-leaf parsley |