Cook the pasta: Bring a large pot of salted water to a boil. Cook pasta until al dente, then drain and reserve ½ cup pasta water.
Cook the chicken: Season chicken breasts with salt, pepper, and Italian seasoning. Heat olive oil in a skillet over medium heat. Cook chicken for 5–6 minutes per side until golden and cooked through. Remove and slice into strips.
Make Alfredo sauce: In the same skillet, melt butter and sauté garlic until fragrant. Add heavy cream and simmer for 2–3 minutes. Stir in Parmesan cheese and nutmeg until sauce is creamy.
Combine: Add cooked pasta and chicken to the skillet. Toss until everything is well coated. Add reserved pasta water if sauce is too thick.
Serve: Garnish with fresh parsley and extra Parmesan. Serve hot with garlic bread or salad.