Preheat oven to 400 degrees and spray a rimmed baking sheet with cooking spray.
Trim chicken tenders, then place them in a large bowl and toss with pesto, olive oil, and black pepper. Arrange chicken in a single layer on one end of the prepared baking sheet.
Trim and cut up the asparagus, halve any larger mushrooms, and chop the onion. Toss the veggies with pesto, olive oil, and black pepper, then arrange them in as close to a single layer as possible on the other end of the baking sheet.
Bake at 400 degrees for 25 minutes, stirring veggies and flipping chicken over halfway through.
Top everything with Parmesan and broil for two minutes.
Notes
The veggies come out crisp-tender here, which is how I like them. If you’d like yours cooked a little softer, simply pre-bake them for a few minutes before adding the chicken to the baking sheet.