Steps
1. Season the chicken leg quarter with salt and pepper.
2. In a large pan, heat some oil over medium heat and brown the chicken on all sides.
3. Remove the chicken from the pan and set aside.
4. In the same pan, add the onion, garlic, carrot, and celery. Sauté until the vegetables are softened.
5. Pour in the beer and add the thyme sprig.
6. Return the chicken to the pan and bring the liquid to a simmer.
7. Cover the pan and let the chicken cook for about 45 minutes or until it is cooked through and tender.
8. Remove the chicken from the pan and strain the liquid, discarding the vegetables.
9. Return the liquid to the pan and simmer until it reduces and thickens slightly.
10. Serve the chicken with the reduced beer broth as a sauce.