Heat oil in a large stock pot over medium-high heat. Add garlic, onion, carrots, and celery and saute 2 minutes. Add chicken and cook until chicken is golden brown on all sides. Add thyme and stir to coat. Add broth, salt and black pepper, increase heat to high and bring to a boil. Partially cover and boil for 5 minutes. Stir in the frozen peas.
Meanwhile, in a medium bowl, combine flour, cornmeal, sage, baking powder, baking soda, salt, and pepper. Add buttermilk and oil and stir with a fork until mixture comes together. Using a spoon or a small ice cream scoop, drop 8 golf ball size dumplings into simmering liquid. Cover pan and cook for 5 minutes (without lifting lid), until dumplings are puffed up and cooked through.