Heat the oven to 450°F with a rack in the middle.

Line a large rimmed sheet pan with parchment paper for easier cleanup.

Put the cabbage wedges and carrot sticks on the sheet pan.

Drizzle 2 tablespoons of the olive oil over the vegetables. Sprinkle them with 1 teaspoon of the salt and 1/2 teaspoon of the black pepper.

Use your hands to coat the vegetables well, then spread them into a single layer. Put the cabbage wedges cut-side down where you can.

Roast the vegetables for 15 minutes so they get a head start.

While the vegetables roast, stir the panko, Parmesan, garlic powder, the remaining 1/2 teaspoon salt, and the remaining 1/4 teaspoon black pepper in a shallow bowl or pie plate.

Put the chicken cutlets on a plate and pat them dry with paper towels so the coating will stick better.

Spread the Dijon mustard over both sides of each chicken cutlet.

Press each chicken cutlet into the Parmesan-panko mixture, turning to coat both sides and pressing lightly so the crumbs cling. Set the coated cutlets back on the plate.

Carefully take the sheet pan out of the oven. Turn the carrots with a spatula and flip the cabbage wedges so the second cut side can brown.

Push the vegetables toward the outer edges of the sheet pan to make space in the middle. Put the coated chicken cutlets onto the open spaces on the pan.