Cook the Chicken: Heat olive oil in a large skillet or Dutch oven over medium-high heat. Season chicken cubes with Italian seasoning, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Add chicken to the hot skillet and cook until golden brown and cooked through, about 5-7 minutes. Remove chicken from the skillet and set aside.
Cook the Gnocchi: Bring a large pot of salted water to a boil. Add the potato gnocchi and cook according to package instructions, typically 2-3 minutes, or until they float to the surface. Drain well and set aside. Avoid overcooking the gnocchi, as it can make them mushy.
Prepare the Alfredo Sauce: In the same skillet (no need to clean), melt butter over medium heat. Add minced garlic and cook for 1 minute until fragrant, being careful not to burn it. Pour in the heavy cream and bring to a gentle simmer, stirring constantly for about 3-5 minutes, allowing it to thicken slightly. Reduce heat to low. Gradually stir in the grated Parmesan cheese, a handful at a time, until completely melted and the sauce is smooth. Stir in the optional nutmeg, and season with additional salt and pepper to taste. If the sauce is too thick, a splash of warm milk or chicken broth can help adjust consistency; if too thin, a bit more Parmesan can help thicken it.
Combine and Serve: Add the cooked chicken and drained gnocchi to the Alfredo sauce. Toss gently to coat everything evenly. Heat through for 1-2 minutes until warmed. Serve immediately, garnished with fresh chopped parsley and extra grated Parmesan cheese.