Whisk together stock and cream of chicken in the bottom of a slow cooker. Add chicken and garlic; season with salt and pepper. Cover and cook on Low for 4 to 5 hours or on High for 2 1/2 hours.
Remove chicken from slow cooker, and add vegetables and heavy cream. Cover and turn crockpot to High and cook 10 minutes.
Meanwhile, chop chicken into bite-sized pieces. Return chicken to the pot and add the noodles. Stir to combine, cover, and cook on High until pasta is tender, about 30 minutes, stirring halfway through. If mixture is too thick, add more stock, a little at a time, as desired.
Stir in 1/4 cup Parmesan cheese. Let stand, covered, for 5 to 10 minutes before serving.
Serve topped with remaining cheese and fresh parsley.
