Prepare the Honey Mustard Dressing: In a small bowl, combine the mustard, honey, salt, pepper, and paprika. Stir until well mixed. Set aside.
Season the Chicken: Rub the chicken breasts thoroughly with the prepared honey mustard dressing. Let them marinate while you prep the vegetables.
Cook the Chicken: Heat 1 teaspoon of olive oil in a large pan over medium heat. Once the oil is hot, place the chicken breasts in the pan and cook for about 5-6 minutes on each side, until they are browned and slightly caramelized from the honey. Push the chicken to one side of the pan.
Sauté the Vegetables: In the same pan, add the chopped red onion, green beans, carrots, and potatoes. Sauté the vegetables for about 5 minutes until they begin to soften, mixing occasionally.
Add Broth and Simmer: Pour the chicken broth over the vegetables, ensuring it reaches the bottom of the pan. Add the sprigs of rosemary. Bring the mixture to a simmer, then reduce the heat to low. Cover the pan and let it cook for 25 minutes or until the potatoes are tender and the chicken is fully cooked.
Serve: Serve the chicken breasts with a generous portion of the sautéed vegetables. The dish is delicious on its own, but you can also pair it with a light salad or some crusty bread if desired.