Rinse the quinoa under cold water, then combine it with 3 cups water in a medium saucepan and bring to a boil over high heat.
Reduce heat to low, cover, and simmer until the water is absorbed and the quinoa is tender, about 12–15 minutes; remove from heat and fluff with a fork.
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 (reserve the rest), 1 tablespoon of the basil (reserve the rest), olive oil, and salt and pepper to taste.
Spread the quinoa mixture evenly into the prepared baking pan, smoothing the top and pressing it down gently.
Sprinkle the reserved cheese and remaining basil evenly over the top.
Bake for 40–45 minutes, until the top is golden and the edges are set. Let cool briefly, then serve.