Melt butter in a large skillet over medium-high heat; add 1/2 cup onion and 1/2 cup celery, and sauté 2 to 3 minutes or until tender.
Whisk in cream of chicken soup, 1/2 cup milk, 1/2 teaspoon dried thyme, and 1/2 teaspoon poultry seasoning; cook over medium-low heat 3 to 4 minutes, stirring occasionally. Add 1 cup Cheddar cheese, stirring constantly, until cheese melts. Stir in cooked chicken, mixed vegetables, salt, and pepper. Cook over low heat, stirring often, 10 minutes or until thoroughly heated.
Spoon warm chicken mixture evenly into Biscuit Bowls.