Place the spring mix in a bowl with cucumber and tomatoes on top. Use a vegetable peeler to shave the carrot onto the top of the salad.
Whisk together ingredients for the vinaigrette and set aside.
Preheat the oven to 400 °F.
Place the bread crumbs, Parmesan cheese, paprika, and garlic powder in a large shallow bowl and stir to mix. Season with salt and pepper to taste.
Place the buttermilk, mustard, and mayonnaise in another shallow bowl and stir to mix.
Toss the potatoes with oil and season well with salt and pepper. Place them into a baking dish.
Dip the chicken breasts in the buttermilk mixture, then dredge them in the bread crumb mixture. Place the breasts over the potatoes.
Bake in the oven until the chicken is cooked to an internal temperature of 160 degrees using a thermometer and the potatoes are tender about 25 minutes.
Dress the salad. Toast the bread.
Serve the chicken with potatoes, salad, bread, and sparkling water.