Preheat the oven to 350 degrees. Combine the quinoa and water in a sauce pan and bring to a boil, then simmer, covered, over low heat until tender, about 15-20 minutes. Set it aside to cool.
Roast the beets in foil for one hour then set aside to cool in a large mixing bowl.
When the beets are cool enough to handle, peel and chop them into small pieces. Place them in a large bowl and add the butternut squash, the quartered cherry tomatoes, and the beans.
In a small bowl, whisk together the olive oil, vinegar, lemon juice, mustard, salt, pepper, oregano, and basil. Gently fold the quinoa into the mixed vegetables, then drizzle the bowl with dressing. Serve immediately or portion into containers to take as leftovers.