Pat the chicken dry with paper towels. Sprinkle 1 tablespoon of kosher salt evenly over the chicken, including inside the cavity. Set aside, uncovered.
In a small bowl, combine softened butter, chopped dill, parsley, garlic, and 1 teaspoon kosher salt. Mix until smooth.
Stir 3 tablespoons white vinegar into the pickle juice and set aside.
Heat the oven to 400°F.
Carefully loosen the skin of the chicken using your fingers. Spread the compound butter evenly under the skin, ensuring it covers the breast and thighs. Place any remaining butter inside the cavity along with the halved garlic and shallot.
Arrange mini potatoes and shallot wedges in a single layer in a 9–10-inch cast iron pan. Sprinkle with kosher salt. Leave a small section of the pan clear to make basting easier. Position the chicken on top of the potatoes and shallots. Pour the pickle brine evenly over the chicken.
Roast for 1 hour and 30 minutes, basting every 30 minutes with the pan juices. If the chicken starts to brown too quickly, tent it loosely with foil.
Insert an instant-read thermometer into the thickest part of the thigh (avoiding the bone). The chicken is done when it reads 165°F. Remove the chicken from the oven and let it rest for 20–25 minutes, loosely tented with foil.
Adjust the pan juices by adding a splash of vinegar, if desired.
Carve the chicken and serve with roasted potatoes and shallots. Garnish with fresh dill and drizzle with pan juices for extra flavor.
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