Preheat oven to 425°F.
Cut chicken into uniform pieces, about 1 1/2 inches around, and place in large bowl. Sprinkle cornstarch on top of the chicken and mix until chicken pieces are evenly coated.
Add lemon juice, pesto, and 1 Tbsp. olive oil to the chicken and stir to cover all the pieces uniformly. Let sit while preparing asparagus.
Place prepped asparagus and onion in a one gallon Ziploc bag or bowl.
Add the remaining olive oil (4 tsp.), parmesan cheese, salt, and pepper to the asparagus and onion. Close the zipper bag and mix the ingredients by gently kneading and rubbing the bag (or mix in a bowl by hand).
Dump the asparagus/onion mixture onto a large rimmed sheet pan and spread out to the edges, leaving space in the middle for the chicken. Pour chicken onto the middle of the pan and spread it out evenly. Place grape tomatoes on top of the chicken and asparagus, along with the garlic cloves.
Bake in preheated 425°F oven for 25 to 30 minutes (or longer if needed) until chicken is done.
Remove from oven and serve immediately. (I like to serve it over whole grain penne pasta tossed with pesto).