Pat the chicken dry with a paper towel. Season with salt and pepper.
In a small bowl, mix together 1 teaspoon of the mustard and the 1 tablespoon of the olive oil. Generously season the chicken and rub with the mustard/oil mixture. Let the chicken marinate for least 30 minutes.
Meanwhile, slice the onion into thin slices. Core the apple and slice into small wedges. Set aside.
Heat the other tablespoon of blood orange olive oil in a large skillet over medium-high heat. Add the chicken to the pan skin-side down and cook until browned. Flip and cook until cooked through. Transfer to a plate and cover with foil.
Preheat the oven broiler.
In a small bowl, stir together the apple vinegar, broth, and the remaining mustard. Set aside.
Add the sliced onion to the skillet, and cook until just translucent. Add the apple slices, and cook for 2-3 minutes until the apples are slightly tender and begin to turn golden.
Return the chicken to the pan skin-side up and pour the vinegar/broth mixture over the top. Let it cook for 5-6 minutes or until the liquid is reduced by half. Transfer the chicken to the oven and broil for 4-5 minutes, until the skin is crispy and golden-brown.