Spray a 6-quart Crock-Pot with cooking spray. Leave fat on thighs; it will render easily after cooking. If you are using breasts, cut each breast into 2–3 pieces.
To the Crock-Pot, add everything listed under "Add First."
Stir well. Cover and cook until the chicken shreds easily, on high for 3–5 hours or low for 4–6 hours.
Remove the chicken and shred with two forks. Gradually add freshly shredded cheese, stirring until melted. Stir in the half-and-half, then return the shredded chicken to the soup. Taste and adjust salt and pepper as needed.
Ladle soup into bowls and top with desired toppings.
