Place a large high-sided skillet with a tight-fitting lid over medium-high heat and melt butter. Add chicken, salt and pepper and cook about 8-10 minutes until chicken is nicely browned and cooked. Remove chicken to a plate. Cover with foil to keep warm and set aside.
Return skillet to heat and add garlic to remaining oil. If necessary, add a bit more butter and cook garlic for about 30 seconds, just to soften. Add chicken broth and pasta and bring to a boil.
When liquid boils, reduce heat to low, cover and cook about 10-12 minutes until pasta is tender but still firm, stirring occasionally. Once pasta is cooked through, there will probably still be as much as 1 cup of liquid still in the pan, which is normal.
Add half-and-half and cream cheese and stir until completely combined and the cream cheese is melted. Allow the sauce to come to a bubble, then remove from heat and stir in Parmesan cheese and reserved chicken.
Replace the lid and allow dish to rest, covered, for 5 minutes to allow sauce to thicken and chicken to re-heat. Prior to serving, give pasta a stir, season to taste with salt and fresh black pepper and sprinkle with chopped parsley. If the sauce gets a bit too thick, just thin it with a touch of milk.