Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Trim, peel, and cut carrots on a diagonal into 1-inch-thick pieces. Trim and thinly slice mushrooms. Trim and thinly slice scallions, separating whites from greens.

Toss carrots on a baking sheet with a drizzle of oil, salt, and pepper. Roast on top rack until tender, 25-30 minutes. Meanwhile, dice potatoes into ½-inch pieces (peel first for a smoother texture). Place in a large pot with enough salted water to cover by 2 inches. Bring to a boil and cook until tender, 15-20 minutes. Reserve ½ cup potato cooking liquid; drain and return potatoes to pot.

While potatoes cook, pat chicken dry with paper towels and season all over with salt and pepper. Heat a drizzle of oil in a large pan over medium-high heat. Add chicken and cook until browned and cooked through, 3-5 minutes per side. Turn off heat; transfer to a plate.

Heat pot with drained potatoes over low heat; add 1 TBSP butter (2 TBSP for 4 servings) and half the sour cream (you’ll use the rest in the next step). Mash potatoes until smooth and creamy, adding splashes of reserved potato cooking liquid as needed. Season with salt and pepper.

Heat a drizzle of oil in pan used for chicken over medium-high heat. Add mushrooms and scallion whites; season with salt and pepper. Cook, stirring, until softened, 2-4 minutes. Stir in stock concentrate and ¼ cup water (⅓ cup for 4 servings). Bring to a boil, then reduce to a low simmer. Cook until slightly thickened, 1-2 minutes. Turn off heat. Stir in 1 TBSP butter and remaining sour cream. Season with salt and pepper.

Heat pan with sauce over mediumlow heat; add chicken and spoon sauce over. Evenly top chicken with Monterey Jack. Cover pan until cheese has melted, 1-2 minutes. Divide chicken, carrots, and potatoes between plates. Spoon remaining sauce over chicken and potatoes. Garnish with scallion greens and serve.