Add the chicken: Place the chicken breasts in the bottom of the slow cooker and season with the black pepper.
Make the sauce smooth: In a saucepan over medium heat, melt the butter, then whisk in the cream cheese, golden mushroom soup, chicken broth, and Italian dressing mix. Stir until the cream cheese melts and the sauce is smooth.
Pour and add mushrooms: Pour the warm sauce evenly over the chicken and scatter the sliced mushrooms on top.
Cook low and slow: Cover and cook on low for 4 to 6 hours, until the chicken is tender and reaches 165°F on a thermometer at its thickest point.
Cook the pasta: Near the end of the cook time, boil the angel hair pasta in salted water according to the package directions until just tender, then drain.
Slice or shred: Slice the chicken into pieces or shred it right in the sauce, then stir to coat it in all that creamy sauce.
Serve: Spoon the chicken and sauce over the angel hair pasta, sprinkle with parsley, and serve warm.
Notes
Warm the butter, cream cheese, soup, broth, and dressing mix on the stove until smooth before pouring over the chicken so the sauce doesn't turn lumpy. Cook the chicken to an internal temperature of 165°F.