Prepare the pasta water. Bring a large stockpot of generously-salted water to a boil.
Cook the chicken (optional). Meanwhile, season the chicken breasts generously on both sides with salt and pepper. Heat the oil in a large nonstick sauté pan over medium-high heat. Add the chicken breasts and sauté for 4-6 minutes per side, until the chicken is cooked through. Transfer the chicken to a clean plate and let it rest for at least 5-10 minutes before slicing into pieces.
Cook the pasta. Add the pasta to the boiling water and cook until *just* al dente. Drain.
Sauté the garlic. While the pasta is cooking, melt the butter in the same sauté pan (or you can cook the sauce in a separate pan, simultaneously with the chicken) over medium-high heat. Add the garlic and sauté for 1 minute, stirring frequently. Whisk in the flour and cook, stirring frequently for 1 minute.
Combine. Whisk in the half and half, salt, white pepper and nutmeg until the mixture is smooth. Continue cooking until the sauce nearly reaches a simmer and thickens. Turn off the heat. Add the cheese and whisk until smooth. Taste and season with additional salt and white pepper if needed.
Toss. Combine the drained pasta with the sauce either in the stockpot or in the sauté pan and toss until evenly coated.
Serve. Serve immediately with the chicken and enjoy!