Add the chicken breast, cream cheese, cubed butter, garlic cloves, salt, pepper, chicken broth, and heavy whipping cream into the slow cooker. Cook on high for 2-3 hours or low for 4-5, until the chicken breast is fully cooked.
Remove the chicken and shred, return to the crockpot along with the pasta, parmesan cheese and cook on high for about 35-40 minutes, or until the pasta is fully cooked through.
Top with freshly grated parmesan and chopped greens and serve.
