Coat the insert of a 6-quart slow cooker with a thin film of butter or nonstick spray. Add the onion, carrots, celery, mushrooms, and garlic in an even layer.

Season the chicken pieces with 1 teaspoon salt and 1/2 teaspoon pepper, then scatter them over the vegetables. Whisk the apple cider, chicken broth, Dijon, Worcestershire, poultry seasoning, and bay leaves together until smooth and pour into the slow cooker.

Cover and cook on HIGH for 45 minutes, keeping the lid closed so the cooker maintains heat. For a longer schedule, cook this base on LOW for 2 to 2 1/2 hours instead, then switch to HIGH before adding the topping.

While the chicken base cooks, mash the softened butter with 3 tablespoons flour until it forms a smooth paste. In a separate bowl, whisk 1 1/2 cups flour, baking powder, baking soda, 1/2 teaspoon salt, and 1/2 teaspoon pepper for the biscuit topping.

Cut the cold butter into the biscuit flour mixture with your fingertips until the pieces are pea-sized. Stir in the buttermilk, 2 tablespoons parsley, and lemon zest just until a shaggy dough forms; do not overmix.

Quickly open the slow cooker. Discard the bay leaves, stir in the butter-flour paste, heavy cream, and frozen peas, then smooth the chicken mixture into an even layer.

Drop the biscuit dough over the top in 12 small mounds, leaving a little space between them. Cover and cook on HIGH for 20 minutes without lifting the lid, until the biscuits are puffed and set on top.

Turn off the slow cooker and let the cobbler stand uncovered for 5 minutes so the sauce settles and thickens slightly.

Sprinkle with the remaining parsley and crushed butter crackers. Serve scooped into shallow bowls, making sure each portion gets chicken, vegetables, sauce, and biscuit topping.