Preheat oven to 400 degrees and line a baking sheet with parchment paper.
Toss the diced butternut squash, red peppers, and green beans in olive oil and spread in a single layer on prepared baking sheet.
Roast veggies in oven for 20-25 minutes, rotating baking sheet halfway through, until they are tender.
While veggies are roasting, combine the quinoa with broth in a medium saucepan. Bring to a boil, then reduce to a simmer, cover, and cook until quinoa is tender and broth is absorbed.
Toss the cooked quinoa and roasted veggies together in a large bowl. Let cool slightly before adding in grated parmesan (if desired) and feeding to your dog.