Melt butter in a skillet over medium high heat. Add chicken, skin-side down, and sear both sides until golden brown, about 2-3 minutes per side; set aside.
Add garlic to the skillet and cook, stirring frequently, until golden brown, about 4-5 minutes. Stir in chicken broth and bring to a boil. Add chicken and sprinkle with thyme. Cover, reduce heat, and simmer until chicken is cooked through, about 25-30 minutes; set aside chicken, reserving the juices in the skillet.
In a small bowl, whisk together flour and milk. Whisk in flour mixture to the skillet until slightly thickened, about 1-2 minutes; season with salt and pepper, to taste.