In a Dutch oven, bring potatoes, 3 teaspoons salt, and water to cover to a boil over medium-high heat. Cook until slightly tender, about 10 minutes; drain.
In a 12-inch cast-iron skillet, melt butter over medium-high heat. Sprinkle both sides of chicken with pepper and remaining 1 teaspoon salt; add to skillet. Sear until golden brown, about 5 minutes per side. Remove from skillet.
Add onion and garlic halves to skillet; sauté until tender, about 5 minutes. Remove garlic halves. Stir in flour and thyme; cook for 1 minute. Stir in wine, broth, and mustard; cook until slightly thickened, about 5 minutes. Stir in cheese until melted. Add chicken, potatoes, and garlic halves to skillet.
Bake until a meat thermometer inserted in thickest portion of chicken registers 165°, 30 to 35 minutes. Garnish with thyme and pepper, if desired.
Recipe by Southern Cast Iron at https://southerncastiron.com/garlic-chicken-with-red-potatoes/