Adjust rack to middle position (middle and top positions for 4 servings) and preheat oven to 425 degrees. Wash and dry produce.

Trim, peel, and cut carrots on a diagonal into ½-inch pieces.

In a small bowl, combine smoked paprika, garlic powder, and 1 TBSP kosher salt (2 TBSP for 4 servings).

Place 2 TBSP plain butter (4 TBSP for 4) in a medium bowl. Cover with plastic wrap and microwave until butter has melted, 30-60 seconds. Add maple syrup, mustard, and a pinch of salt; stir to combine.

Reserve 2 tsp maple-mustard sauce (4 tsp for 4) in a separate small bowl (you'll use it in the next step).

Pat chicken* dry with paper towels. Rub smoky salt all over chicken (make sure to season underneath the skin and in the cavity too!). Brush reserved maple-mustard sauce all over chicken; place on one side of a baking sheet (for 4 servings, spread out across entire sheet).

Roast on middle rack until chicken is just beginning to brown, 10 minutes (you'll add more to the sheet then).

Meanwhile, once chicken has roasted 10 minutes, carefully toss carrots on empty side of same sheet with a drizzle of oil, thyme, salt, and pepper. (For 4 servings, leave chicken roasting; add carrots to a second sheet and roast on top rack.)

Return to middle rack and roast until carrots are browned and tender and chicken is nearly cooked through, 15-20 minutes more (you'll finish the chicken in Step 6).

While chicken and carrots roast, peel and dice potatoes into ½-inch pieces. Place potatoes in a medium pot (large pot for 4 servings) 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 (1 cup for 4), then drain and return potatoes to pot. Add sour cream and garlic herb butter. Mash with a potato masher or fork until smooth and creamy, adding splashes of reserved potato cooking liquid if necessary. Season with salt and pepper. Keep covered off heat until ready to serve.

When chicken is almost done, remove sheet from oven (for 4 servings, if carrots are done, remove from oven) and carefully pour remaining maple-mustard sauce over chicken. Return to middle rack and roast until chicken is charred and cooked through and carrots are tender, 5 minutes more. TIP: To ensure chicken is cooked through, insert a thermometer into the innermost part of the thigh and breast (avoiding any bones). Once chicken is cooked, the bones may still appear pink—this is OK!

Remove from oven; let chicken rest at least 5 minutes.

Transfer mashed potatoes to a large plate; top with chicken and carrots. Pour any remaining sauce from baking sheet over chicken and serve.