Place the chicken breasts in an even layer in the bottom of the slow cooker.
In a medium bowl, whisk together the softened cream cheese, butter, cream of chicken soup, minced garlic, chicken broth, and Italian dressing seasoning until mostly smooth.
Pour the sauce mixture over the chicken, spreading it evenly to coat.
Cover and cook on low for 4 to 6 hours, until the chicken is tender and fully cooked.
Shred the chicken directly in the slow cooker using two forks and stir to combine with the sauce.
Cook the angel hair pasta according to package directions. Drain well.
Serve the creamy chicken over the pasta and spoon extra sauce on top.