Season chicken with salt and pepper, to taste.
Heat oil in a large skillet over medium-high heat. When oil shimmers, add chicken and cook for at least 5-6 minutes (or until nicely browned on the first side). Flip the chicken breast over and brown on the second side (about 6-10 more minutes). The chicken is done when it reaches an internal temperature of 165 degrees F. Remove chicken and set aside on a plate. Cover with foil to keep warm.
Add onion to the skillet and cook, stirring frequently, until tender (about 3-5 minutes). Scrape up all of the browned chicken bits from the bottom of the pan so that the flavor incorporates into your sauce! Add garlic and cook, stirring, for one more minute.
Stir in the Dijon, soup and water; bring to a boil. Reduce heat to low, stir in spinach, salt, pepper and nutmeg; cook for about 3 minutes (or until spinach is warmed through). Stir in half-and-half and simmer for 3-4 more minutes (do not boil). Add extra half-and-half, as needed, to thin sauce to reach desired consistency. Taste the sauce and season with additional salt and pepper, if necessary.
Return chicken to the skillet and spoon sauce over top. Garnish with grated Parmesan cheese and fresh herbs, if desired.