Pat the chicken dry with paper towels and season with salt and pepper. In a large skillet over medium-high heat, melt the butter. Add the chicken thighs in, skin-side down, and sear both sides until they are golden brown, about 2-3 minutes per side. Transfer to a plate.
Add the garlic cloves to the skillet, stirring frequently, cook until they are golden brown, about 4-5 minutes. Stir in the chicken broth and thyme and bring to a boil.
Return chicken to skillet and simmer until a thermometer inserted reads 165 degrees, about 25 to 30 minutes. Transfer chicken to a serving platter, reserving the juices remaining in the skillet.
In a small bowl, whisk together the flour and the milk. Whisk the flour-milk mixture into the skillet until the sauce is thickened slightly, about 1 to 2 minutes. Season to taste with salt and pepper.
Pour the sauce over the chicken and serve immediately.