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Step 1
Heat oil in a large heavy Dutch oven over medium-high heat. Season chicken breasts with salt and pepper. Place chicken in Dutch oven and cook until brown on both sides, 12-15 minutes total. Transfer to a plate and set aside.
Step 2
Place leeks and onion in same pot and sauté until tender, about 8 minutes. Add garlic and sauté until tender, about 2 minutes. Stir in broth, wine, Dijon mustard, and minced thyme and bring to a simmer. Return chicken to pot. Cover and simmer over medium-low heat until chicken is cooked through, about 15 minutes.
Step 3
Transfer chicken to plates. Bring liquid in pot to a boil; cook until sauce is thickened and glossy, about 15 minutes. Whisk in butter and season with salt and pepper. Spoon sauce over chicken and garnish with thyme leaves.