1. First, using a strainer, rinse the quinoa under cold water. Add quinoa, water, and salt to a medium saucepan and bring to a boil over medium heat. Boil for 5 minutes. Turn the heat to low and simmer for about 15 minutes, or until water is absorbed. Remove from heat and fluff with a fork.
2. While the quinoa is cooking, place the zucchini, yellow squash, and green beans in a large bowl. In a small bowl, whisk together balsamic vinegar, olive oil, and garlic. Pour balsamic dressing over the vegetables and toss until vegetables are well coated. Season vegetables with salt and pepper, to taste.
3. Heat grill to medium-high heat. Place the vegetables in a grill basket. If you don't have a grill basket, spread out the vegetables on a large sheet of aluminum foil. Add a top sheet of foil and crimp the edges of the sheets together to make a packet. Place on the hot grill and cook until tender crisp, about 10 minutes. Remove the vegetables from the grill.
4. Place the cooked quinoa in a large bowl. Add the grilled summer squash, green beans, basil, and stir. Drizzle with extra balsamic vinegar and olive oil, if desired. Season with salt and pepper, to taste. Garnish dish with Parmesan cheese, if using. Serve warm.