Prepare the slow cooker by coating it with a light coating of cooking spray.
Place chicken breasts in the prepared slow cooker and set aside.
In a small saucepan, melt the butter over medium heat and cook garlic for 2-3 minutes or until fragrant.
Add the cream of chicken soup, cream cheese, Italian dressing mix, chicken broth, and white wine and whisk until melted and smooth. (About 3-5 minutes)
Pour the sauce evenly over the chicken in the slow cooker.
Cover and cook on low for 5-6 hours or until the chicken is tender and fully cooked.
About 20 minutes before serving, cook the angel hair pasta according to package instructions. Drain and toss with the butter to prevent sticking.
Shred or slice the chicken, then stir the sauce in the slow cooker to combine. Serve the chicken and sauce over the cooked pasta.
Garnish with fresh parsley before serving.