Chicken Alfredo with Pasta - Miz En Place

Ingredients

• 8 ounces dried fettuccine pasta
• 1 pound skinless chicken breasts
• 1 tsp kosher salt (divided)
• 1/2 tsp freshly ground black pepper (divided)
• 2 tbsp canola oil
• 8 tbsp unsalted butter (divided)
• 2 cloves garlic (minced)
• 1 cup heavy cream
• 1 cup finely grated Parmesan cheese (plus more for serving)
• 1/4 tsp freshly grated nutmeg
• Coarsely chopped fresh parsley leaves (for serving)