Preheat oven to 400ºF.
Place chicken in a pan with 1/2 of the onion and bay leaf. Bring to a boil then reduce heat to simmer. Gently poach chicken until cooked through. Remove from liquid and dice or shred with forks in a mixing bowl.
Meanwhile, heat a small skillet over medium-high heat. Add mushrooms and brown 5 minutes. Finely chop remaining 1/2 onion and add to the pan along with the celery. Season with salt and pepper, and cook until tender, a few minutes more. Add frozen veggies and heat through, a minute or 2 more. Add veggies to bowl with shredded or cut chicken.