Layer the base: Add onion, carrots, celery, and potatoes to the slow cooker. Sprinkle in garlic, thyme, rosemary, salt, pepper, and the bay leaf.
Add the chicken: Place chicken breasts or thighs on top of the veggies. Pour in the chicken broth.
Cook low and slow: Cover and cook on Low for 6–7 hours, or on High for 3–4 hours, until the chicken is fork-tender and the vegetables are soft.
Make a quick roux: About 30 minutes before serving, melt butter in a small saucepan over medium heat.
Whisk in the flour and cook for 1–2 minutes until lightly golden. Slowly whisk in the milk (and heavy cream if using) until smooth and thickened, 3–5 minutes.
Shred and thicken: Remove the chicken to a cutting board and shred with two forks. Discard the bay leaf.
Stir the roux mixture into the slow cooker. Add the shredded chicken back in.
Finish with veggies: Stir in the frozen peas and corn. Cover and cook on High for 20–30 minutes to thicken and heat through.
Adjust seasoning with salt, pepper, and lemon juice if using.
Bake the topping: While the filling finishes, bake biscuits or puff pastry according to package directions until golden.
Serve: Spoon the pot pie filling into bowls and top with a biscuit or a square of puff pastry. Garnish with fresh parsley.