Combine the chicken, beans, butter, garlic, parsley, shallot, lemon juice, 2 teaspoons salt and several generous grinds of pepper in a 6- to 8-quart slow cooker. Cook on low until the chicken is tender and the flavors have mellowed, about 4 hours.
Break the chicken into large pieces using two forks. Stir in the sour cream.
Serve the stew topped with croutons and more parsley.
