Heat 2 tablespoons butter or oil in a large pot over medium heat
Add 1 diced onion, 2 diced carrots, and 2 diced celery stalks
Cook until softened, about 5 minutes
Stir in 2 minced garlic cloves and cook for 30 seconds
Add 4 cups chicken broth, 2 cups cooked shredded chicken, 1 teaspoon salt, 1/2 teaspoon black pepper, and 1 teaspoon dried thyme
Bring to a simmer
Stir in 1 cup milk or half-and-half
Cut 4 to 6 refrigerated biscuit dough pieces into quarters
Drop biscuit pieces into the simmering soup
Cover and cook on low heat for 10 to 15 minutes
Stir gently once or twice to prevent sticking
Cook until biscuits are puffed and cooked through
Add 1 cup frozen peas if desired
Taste and adjust seasoning
Serve hot