Heat oven to 400° F. Cook the quinoa according to the package directions.
Meanwhile, heat the oil in a large skillet over medium heat. Add the onion, ½ teaspoon salt, and ¼ teaspoon pepper and cook, stirring frequently, until softened, 3 to 5 minutes. Add the chili powder and cook, stirring, until fragrant, about 1 minute. Add the beans, broth, and garlic and simmer, stirring occasionally, until most of the liquid has been absorbed, 2 to 4 minutes more. Fold in the spinach.
Dividing evenly, top the tortillas with the quinoa (about ½ cup each), bean mixture (about ½ cup each), and Cheddar (about ⅓ cup each). Roll up into burritos; wrap each in heavy-duty foil and place on a baking sheet.
Bake the burritos until warmed through, 15 to 20 minutes. Serve with the salsa, sour cream, and sliced avocado.
The uncooked wrapped burritos can be frozen in freezer bags for up to 3 months. To reheat, remove from foil and microwave on high until warmed through.