Preheat the oven to 375°F. Lightly season the chicken breasts with 1 teaspoon of kosher salt and a dash of freshly ground black pepper. In a large, oven-safe skillet, heat 1 tablespoon of vegetable oil over medium-high heat. Place the chicken in the skillet, skin-side down, and cook until the skin becomes golden brown, approximately 5 minutes. Transfer the skillet to the preheated oven, keeping the chicken skin-side down, and roast until a thermometer inserted into the thickest part reads 165°F, about 25 minutes. Once cooked, place the chicken on a cutting board and allow it to rest for 5 minutes.

To prepare the dressing, whisk together the sherry vinegar, Dijon mustard, and honey in a large mixing bowl. Slowly pour in the remaining 1/3 cup of vegetable oil, whisking continuously until the mixture is emulsified and smooth.

Remove the roasted chicken from the bone and slice it into pieces. Thinly slice the Gala apples and combine them with the dressing, chopped walnuts, escarole, and endive in the bowl. Season the mixture with salt and pepper to taste. Gently toss the ingredients until evenly coated. Arrange the sliced chicken over the salad and sprinkle the shredded aged cheddar on top. Serve with a side of multigrain bread if desired.