Position an oven rack in the center of the oven and preheat to 400 degrees F. Line a rimmed baking sheet with foil and set aside.
Place the squash in a medium bowl and add 3 tablespoons of the oil, the thyme and 2 teaspoons of salt and season with pepper to taste. Mix until the squash is well coated. Transfer to the prepared baking sheet and spread squash out into a single layer. Roast until a paring knife slides into the squash with no resistance, about 30 minutes, stirring about halfway through the cooking time. Put the pistachios on a small baking sheet and toast until fragrant, about 5 minutes.
Meanwhile, rinse the quinoa in cold water in a fine-mesh strainer. Bring the broth or water to a boil and stir in the quinoa. Simmer, uncovered, until a small white spiral becomes visible in each grain, about 9 minutes. Drain the quinoa and transfer it to a medium bowl. Add the remaining 2 tablespoons olive oil, the pistachios, cranberries, vinegar, 1/2 teaspoon salt and pepper to taste.
Place the spinach in a large mixing bowl and toss with the hot squash until slightly wilted. Add the quinoa mixture and toss again. Serve warm or at room temperature.