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 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, 5-7 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 later). Using a potato masher or fork, 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 medium low; 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.