Preheat oven to 375°F and position rack in the upper third.
Place chicken cutlets on one side of a large sheet pan.
Brush with 1 tablespoon olive oil and season with Italian seasoning, ½ teaspoon salt, and ¼ teaspoon pepper.
Bake for 5 minutes.
In a small bowl, mix balsamic vinegar, garlic powder, and remaining olive oil.
Remove chicken from oven. Add asparagus, red onion, and capers to the empty side of the pan.
Drizzle half of the balsamic mixture over vegetables and toss to coat.
Flip the chicken and drizzle with the remaining mixture.
Switch oven to broil on high and cook for about 10 minutes, until the chicken reaches 165°F and asparagus is tender-crisp.
Drizzle extra balsamic vinegar before serving for enhanced flavor.