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Step 1
Preheat the oven to 375°F with a rack in the center position.
Step 2
In a small bowl, stir together the whole-grain mustard, 1 tablespoon of the olive oil, apple cider vinegar, brown sugar, and minced garlic. Sprinkle the chicken all over with the salt and pepper. Rub the chicken all over with the mustard mixture.
Step 3
Arrange the leeks and sliced garlic in the bottom of a large cast-iron skillet or braiser. Drizzle with 1 tablespoon of the olive oil, top with the lemon slices, and pour in the wine. Set the chicken, breast side up, on top of the bed of leeks and lemons. If desired, tie the legs together with kitchen string and tuck the wing tips under the body of the chicken.
Step 4
In a large bowl, toss the potatoes with the remaining 1 tablespoon of olive oil and remaining 1 teaspoon of salt. Arrange the potatoes around the chicken.
Step 5
Roast the chicken for 15 minutes per pound. Begin checking for doneness when 20 minutes remain (see Note). Transfer the chicken to a cutting board and let rest for 10 minutes before carving.
Step 6
Stir the tarragon and cold butter into the leeks and potatoes until the butter is melted. Serve the chicken drizzled with the pan sauce.