01 - Place chicken breasts in the bottom of the slow cooker in a single, even layer.
02 - Melt butter in a medium saucepan over medium heat. Add softened cream cheese and stir continuously until completely smooth and melted.
03 - Add cream of chicken soup, Italian dressing mix, and chicken broth to the saucepan. Stir until thoroughly combined and no lumps remain.
04 - Pour the prepared sauce evenly over the chicken breasts, ensuring all pieces are coated.
05 - Cover and cook on LOW setting for 4-5 hours, until chicken is tender and reaches an internal temperature of 165°F.
06 - About 20 minutes before serving, cook angel hair pasta in a large pot of salted boiling water according to package directions. Drain well.
07 - Remove cooked chicken from the slow cooker. Shred with forks or leave whole based on preference. Stir the sauce to blend any separated liquids.
08 - Portion cooked pasta onto plates or bowls. Top with chicken and generous sauce. Garnish with fresh parsley and black pepper if desired.