Heat oven to 425 degrees. Brush squash with 2 tablespoons oil and season with salt and pepper. Roast cut side down on two baking sheets until tender and caramelized, 15 to 20 minutes.
Meanwhile, bring quinoa and 2 cups water to a boil in a small pot. Reduce heat and simmer, covered, until tender and water is absorbed, about 15 minutes. Let cool, then fluff with a fork. In a large bowl, combine quinoa, parsley, feta, pistachios, remaining 2 tablespoons oil, and vinegar. Season with salt and red-pepper flakes. Divide filling among squash.