Wash and dry all produce. Adjust rack to upper position and preheat oven to 450 degrees. Pick fronds from dill; discard stems. Finely chop fronds. Cut potatoes into 1/2-inch cubes.

Toss potatoes on a baking sheet with a large drizzle of oil and a pinch of salt and pepper. Roast in oven until browned and tender, 22-25 minutes, tossing halfway through.

Heat a large drizzle of oil in a large pan over medium heat. Pat chicken dry with paper towels. Season all over with salt and pepper. Add to pan and cook until no longer pink in center, 4-6 minutes per side. Turn off heat. Remove chicken from pan and set aside to rest.

While chicken cooks, toss green beans on another baking sheet with a large drizzle of oil and a pinch of salt and pepper. Roast in oven until tender, 10-12 minutes.

Add 1 tsp dill, sour cream, stock concentrates, mustard, and 1/4 cup hot water to pan used for chicken. Stir, off heat, scraping up any browned bits on bottom. Season with salt and pepper. TIP: If sauce seems thick, add more hot water, 1 tsp at a time, until it has a drizzling consistency.

Thinly slice chicken, then divide between plates along with potatoes and green beans. Drizzle sauce over everything. Garnish with remaining dill (to taste—you may want to skip this for the kids).