Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.

Trim, peel, and cut carrots into sticks (like fries; ours were 3 inches long and ⅓ inch thick). Halve buns.

In a shallow dish, combine panko, garlic powder, salt (we used 1 tsp; 2 tsp for 4 servings), and pepper.

Toss carrots on a baking sheet with a large drizzle of olive oil. Season generously with salt and pepper.

Roast on top rack until tender, 15-20 minutes.

Pat chicken* dry with paper towels; place between two large pieces of plastic wrap. Pound with a mallet or rolling pin until chicken is about ½ inch thick. Season all over with salt and pepper.

Brush chicken all over with sour cream. Working one piece at a time, press chicken into panko mixture until fully coated on both sides.

Heat a ⅓-inch layer of oil in a large, heavy-bottomed pan over medium-high heat. Once oil is hot enough that a pinch of panko mixture sizzles when added to the pan, add coated chicken. Cook until crust is golden brown and chicken is cooked through, 5-7 minutes per side. (TIP: Fry in batches if necessary; lower heat if chicken begins to brown too quickly.) Transfer chicken to a paper-towel-lined plate.

AIR FRYER ALTERNATIVE: Coat an air fryer basket with cooking spray; arrange coated chicken side by side in basket. Coat tops of chicken with cooking spray. Air fry at 390 degrees for 6 minutes. Flip chicken and coat again with cooking spray; air fry until cooked through and crispy, 6 minutes more.

In a small bowl, whisk together mayonnaise, honey Dijon dressing, and hot sauce to taste (we used the whole packet). Season with salt and pepper.

Toast buns until golden brown.

Spread top buns with as much honey mustard mayo as you like. Fill buns with chicken.

Divide sandwiches and carrots between plates. Serve with any remaining honey mustard mayo on the side for dipping.