Preheat the oven to 425°F.
Rinse and drain the quinoa thoroughly. In a medium pot, combine the quinoa with 4 cups water and bring to a boil. Reduce to simmer, cover and cook until all the water is absorbed, about 15 minutes. The grains should be soft when done.
When the quinoa is done transfer it to a large bowl to allow it to cool and let extra steam escape.
On a large sheet pan, toss the eggplant, peppers, onion, and garlic with 1/3 cup olive oil, 1 1/2 teaspoons salt, and 1/2 teaspoon of pepper. The vegetables should all be oil-coated.
Roast in the oven for 40 minutes or until soft and browned. Turn the veggies halfway through with a spatula. Remove from the oven and let it cool.
In a small bowl, whisk together the lemon juice, 1/3 cup olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper.
Combine the quinoa, vegetables and dressing into a large bowl and gently toss to mix in the dressing. Add the scallions, feta and basil.
Serve at room temperature or chilled.