Heat oil in a large ovenproof skillet over medium-high heat. Add onion and cook until tender, about 2 minutes. Add chicken, frozen vegetables, and garlic. Sprinkle with salt and pepper. Cook, stirring occasionally, until browned, 6 to 8 minutes.

Pour tomatoes and water into the skillet with the chicken; bring to a boil. Stir in quinoa and cilantro. Cook until quinoa is tender and most of the liquid has evaporated, about 15 minutes; the dish should look thick and saucy. Spread an even layer of Cheddar cheese on top.

Set an oven rack about 6 inches from the heat source and preheat the oven's broiler.

Place skillet into oven and melt Cheddar cheese under the broiler until bubbly and golden, 2 to 3 minutes; be sure to watch carefully to prevent burning.