In a deep skillet or Dutch oven, melt butter over medium-high heat. Add chicken and season with salt and pepper to taste. Brown on each side, 2-3 minutes, then remove from pot.
Add onion and garlic to the pan and sauté until tender, about 5 minutes.
Add flour to the pan. Cook for 1 minute, stirring continuously.
Slowly add water and chicken broth, stirring to combine.
Bring mix to a boil over high heat.
Add carrots, celery, chicken, and accumulated juices to the pan.
Reduce heat to low. Cover and cook for 20 minutes. Add any additional salt and pepper or other spices at this stage.
Remove chicken to a clean serving dish, cover to keep warm.
Combine biscuit mix and milk in a separate bowl.
Once mixed, drop rounded spoonfuls into hot liquid.
Cook uncovered for 10 minutes, then cook covered for 5 minutes.
Ladle stew and dumplings over chicken. Garnish with thyme sprigs.