Preheat oven to 350. Prepare quinoa according to package directions or in a rice cooker. Set aside.
Line 2 baking sheets with foil and spray with grapeseed oil. Place chicken breasts on one sheet. Spread pesto over the tops of them. Place sliced tomatoes over the pesto, and top everything with cheese. Place in oven and let chicken cook for about 35 minutes.
After placing chicken in the oven, trim the woody ends off the asparagus by cutting off the bottom third. Spray second baking sheet with oil and spread asparagus spears out on top. Season with salt and pepper, and spritz with more spray. Add asparagus to oven; it will need about 20 minutes.
Remove asparagus from oven. Change oven over to broiler and put on high heat. Let chicken breasts brown under broiler for 5 minutes. Remove from oven and serve with asparagus and quinoa.
*To make this dish lactose-free, use vegan or dairy-free pesto and cheese.