Melt butter in a large skillet over medium-high heat; add 1/2 cup onion, 1/2 cup celery, and 1/2 cup sliced mushrooms, and sauté 2 to 3 minutes or until tender.
Whisk in cream of chicken soup, 1/2 cup milk, and 1/4 teaspoon dried tarragon; 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, peas and carrots, diced pimiento, salt, and pepper. Cook over low heat, stirring often, 10 minutes or until thoroughly heated.
Spoon warm chicken mixture evenly into Biscuit Bowls.
Chicken Pot Pie in Biscuit Bowls: Substitute 1 (10-ounce) thawed package frozen mixed vegetables for peas and carrots. Add 1/2 teaspoon dried thyme and 1/2 teaspoon poultry seasoning. Omit tarragon, sliced mushrooms, and pimiento. Proceed with recipe as directed.