Wash and dry all produce. Preheat oven to 450 degrees, distributing racks evenly. Slice potatoes into 1/2-inch-thick wedges (like steak fries).

Spread panko on a baking sheet. Toast in oven until golden brown, 2-3 minutes. Transfer to a large bowl or shallow dish, then add Parmesan and a drizzle of olive oil. Season with salt and pepper.

Toss potatoes, a large drizzle of olive oil, rosemary, and a large pinch of salt and pepper on same baking sheet. Bake in oven until deeply browned and crisp, 25-30 minutes, flipping halfway through.

Cut chicken into 1-inch-wide strips. Season all over with salt and pepper. Crack eggs into a medium bowl and lightly beat. Working one piece at a time, dip chicken into eggs, letting excess drip off, then coat in panko mixture, pressing to adhere. Place on a lightly oiled baking sheet.

Toss green beans on another baking sheet with a drizzle of olive oil and a pinch of salt and pepper. Bake green beans and chicken in oven until chicken is no longer pink in center and green beans are tender and slightly crisp at the edges, 12-15 minutes.

Stir together honey and mustard in a small bowl. Divide chicken, potatoes, and green beans between plates. Serve with honey mustard sauce on the side for dipping.