In a glass dish, stir 1/4 cup kosher salt into 4 cups warm water until dissolved to make a brine. Add the chicken and let sit at room temperature 15–30 minutes. Remove chicken, rinse under cold water, and pat dry.
Whisk together honey, Dijon mustard, stone-ground mustard, yellow mustard, and 1 tablespoon olive oil in a small bowl. Reserve 1/4 cup of this sauce to coat the chicken before baking and set the rest aside for serving.
Place the potato cubes in a microwave-safe dish and add enough water to reach about 1/4 inch up the sides. Cover and microwave 6 minutes, then drain.
Transfer drained potatoes to a lightly greased 9x13 baking dish. Add 1 tablespoon olive oil, 3/4 teaspoon salt, and 1/4 teaspoon pepper; toss to coat. Push the potatoes to the sides of the dish to make a space in the center for the green beans.
Toss the green beans with 1 tablespoon olive oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Lay the beans in the center of the baking dish between the potatoes (they may overlap slightly).
In a large bowl, combine garlic powder, onion powder, paprika, dried parsley, 1 teaspoon salt, 1/2 teaspoon pepper, and 1/8 teaspoon cayenne to make the chicken seasoning. Add 1 tablespoon olive oil and mix into a wet rub.
Add the chicken to the bowl and massage the spice mixture into both sides. Coat both sides of each breast with the reserved 1/4 cup honey mustard sauce. Transfer the chicken to the center of the baking dish, spooning any remaining spice mixture or sauce over the top.
Cover the pan with foil and bake at 400°F for 25 minutes. Remove the foil and check the chicken with an instant-read thermometer; if not at 165°F, bake uncovered an additional 10–20 minutes until the internal temperature reaches 165°F.
Let the chicken rest 5–10 minutes before slicing. Serve the chicken with the remaining honey mustard sauce.
