Place the boneless skinless chicken breasts in the bottom of the slow cooker, spreading them into an even layer so they cook uniformly. Add no water or oil; the remaining ingredients will supply the moisture.

Add the cream of chicken soup, cream of celery soup, chicken broth, frozen peas, frozen corn, diced carrots, sliced celery, and diced small onion on top of the chicken. Sprinkle in garlic powder, onion powder, dried thyme, salt, and black pepper so the seasonings distribute during cooking.

Cook on low for 6–7 hours or high for 3–4 hours until the chicken is tender and cooked through, with the mixture visibly bubbling at the edges (visual cue). Keep the lid on to maintain steady temperature.

Remove the chicken from the slow cooker, then shred with two forks until no large pieces remain (visual cue: strands). Return the shredded chicken to the slow cooker.

Stir in the sour cream and mix until the filling looks thick and creamy, about 2–3 minutes after mixing (visual cue: slow spoon trail that holds briefly). Keep the heat low so the sour cream blends smoothly.

Bake the puff pastry or refrigerated biscuits separately according to package directions until golden, with puffed layers or browned tops (visual cue). Let the topping stand briefly so it doesn’t collapse when served.

Serve the filling in bowls topped with the baked pastry or biscuits. Add parsley if desired and pour carefully so steam rises from the filling (visual cue).