Position oven rack in upper third; preheat oven to 375°F.
Place 4 chicken cutlets on one side of a large rimmed baking sheet.
Brush both sides with 1 tablespoon oil; sprinkle with 1 teaspoon Italian seasoning, ½ teaspoon salt and ¼ teaspoon pepper.
Bake for 5 minutes.
Meanwhile, stir 2 tablespoons vinegar, ½ teaspoon garlic powder and the remaining 1 tablespoon oil together in a small bowl.
Remove the chicken from the oven. Preheat broiler to high.
Place trimmed asparagus, ¾ cup red onion and 1 tablespoon capers on the empty side of the pan; drizzle with half the vinegar mixture and toss to coat.
Flip the chicken pieces and drizzle with the remaining mixture.
Broil until the asparagus is tender-crisp and an instant-read thermometer inserted in the thickest part of the chicken registers 165°F, about 10 minutes.
Drizzle with more vinegar, if desired.
