Rinse the quinoa under cold water, then combine with 3 cups water in a medium saucepan and bring to a boil uncovered over high heat.
Reduce heat to low, cover, and simmer until the water is absorbed and quinoa is tender, about 12–15 minutes; fluff with a fork and taste to confirm doneness.
While the quinoa cooks, preheat the oven to 375°F (190°C) and spray a 9x9-inch or 9x13-inch baking pan with cooking spray.
Transfer the cooked quinoa to a large bowl. Stir in the marinara sauce, about two-thirds of the shredded cheese, 1 tablespoon of the basil, olive oil, and salt and pepper to taste.
Spread the quinoa mixture evenly into the prepared baking dish, smoothing the top and pressing down gently.
Sprinkle the remaining cheese and remaining tablespoon of basil evenly over the top.
Bake uncovered for 40–45 minutes, until the top is golden and the edges are set.
Let cool slightly, then serve.