Season chicken with 3/4 tsp salt and pepper to taste. Spritz a very large pan with cooking spray.
Over medium-high heat, sear chicken on both sides until just browned, about 2 minutes per side. Remove chicken from pan and set aside.
Spritz pan with a little more cooking spray and add in bell peppers and onion. Sauté veggies until softened, about 4-5 minutes.
Add garlic and sauté for another minute. Add in white wine and reduce by half. This should take about 2-3 minutes.
Return Chicken to pan. Mix in chicken stock, both milks, and all remaining seasonings. DO NOT ADD PARMESAN. Bring liquids to a boil.
Lay spaghetti on top of the liquid mixture. Push the pasta into boiling liquid until mostly submerged. If you have a smaller-brimmed pot, you may need to break your pasta in half.
Cover pan and reduce heat to medium-low. Cook for 10 minutes, stirring halfway through.
Remove lid, raise heat to medium-high, and cook, stirring often, for about 3-5 minutes, or until pasta is fully cooked but some liquid still remains.
Take pan off heat. Mix in parmesan and let stand to thicken up for a minute or so.