Preheat the oven to 425°F. Lightly spray an 18x13-inch large rimmed sheet pan with nonstick spray.
On the prepared pan, toss together the green beans, potatoes, olive oil, garlic, salt and pepper to taste. Spread the vegetables out in a single layer. Bake until partially cooked, about 20 minutes.
PREPARE THE CHICKEN:
While the vegetables are cooking, season the chicken with the salt and pepper to taste. Put the flour in a shallow plate and put the egg in a medium bowl. Put the panko in another shallow plate. Dredge each chicken cutlet lightly in the flour, then dip in the egg, shaking off the excess. Dredge in the panko, lightly pressing to evenly coat. Set aside on a plate.
Remove the pan of vegetables from the oven, stir them together, the push to one side. Place the chicken on the other side of the pan and spray the tops with olive oil spray. Return to the oven and bake until the chicken is golden and the potatoes are cooked through, about 15 minutes. Switch the oven to broil and broil until the top of the chicken is browned slightly, 1 to 2 minutes. Remove the pan from the oven and squeeze the lemon half over the vegetables.
Top the chicken with the capers and parsley, and serve with the lemon wedges on the side
Notes
Gluten-free adaptions: to make this recipe gluten-free, sub gluten-free flour for the all-purpose and sub gluten-free breadcrumbs for regular.