Make the honey-mustard sauce: In a small bowl, combine the Dijon mustard, honey, 1/2 teaspoon salt, apple cider vinegar and paprika. Stir until smooth.
Season the chicken breasts with the remaining 1 teaspoon salt and the pepper.
Heat 1 tablespoon olive oil in a large oven proof skillet or braiser over medium high heat. When the oil is glistening, sear the chicken until golden brown, about 3 minutes each side. Remove the chicken from the skillet onto a plate.
Add the shallots and fingerling potatoes along with the remaining olive oil into the braiser and toss to combine. Sprinkle with rosemary and place the potatoes in the oven, uncovered, for 15 minutes.
Remove the skillet from the oven. Nestle the chicken (along with any juices from the plate) and the green beans into the par-cooked potatoes in the skillet. Continue cooking for another 15 minutes.
Remove the skillet from the oven and pour the sauce over the chicken, green beans and potatoes, toss to combine. Cook for 10-15 more minutes longer or until the chicken has reached 165°F with an instant-read thermometer.