Adjust rack to top position (top and middle positions for 4 servings) and preheat oven to 425 degrees. Wash and dry all produce. Trim and thinly slice mushrooms. Trim and thinly slice scallions, separating whites from greens. Cut broccoli florets into bite-size pieces, if necessary. Dice potatoes into 1/2-inch pieces; 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 1/2 cup potato cooking liquid, then drain and return potatoes to pot.

Meanwhile, pat chicken dry with paper towels. Lay two slices of prosciutto beside one another on a flat surface. Tightly roll prosciutto around chicken. Repeat with remaining prosciutto and chicken. (TIP: You may have some prosciutto left over; use the rest as you like.) Heat a drizzle of oil in a large pan over medium-high heat. Add wrapped chicken; sear until browned, 2 minutes per side. Turn off heat; add to one side of a lightly oiled baking sheet (for 4 servings, spread out across entire sheet).

Toss broccoli on empty side of same sheet with a drizzle of oil and a large pinch of salt and pepper. (For 4 servings, toss broccoli on a second baking sheet; roast chicken on middle rack and broccoli on top rack.) Roast on top rack until chicken is cooked through and broccoli is browned and tender, 14-16 minutes. (TIP: If chicken is done before broccoli, remove from oven and continue roasting broccoli.) Set chicken aside to rest for a few minutes; slice crosswise.

Heat pot with potatoes over low heat. Mash with 1 TBSP butter and 2 packets sour cream (4 packets for 4 servings; you’ll use the rest later) until smooth and creamy, adding splashes of reserved potato cooking liquid as needed. Stir in scallion greens. Season generously with salt and pepper. Keep covered off heat until ready to serve.

Wash out pan used for chicken. Heat a drizzle of oil in same pan over mediumhigh heat. Add mushrooms and scallion whites; season with salt and pepper. Cook, stirring, until softened, 2-4 minutes. Stir in stock concentrate and 1/4 cup water (1/3 cup for 4 servings). Cook until slightly thickened, 2-3 minutes. Turn off heat. Stir in 1 TBSP butter (2 TBSP for 4) and remaining sour cream. Season with salt and pepper.

Divide potatoes, chicken, and broccoli between plates. Spoon sauce over chicken and potatoes and serve.