Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish and arrange red bell peppers in dish.
Roast peppers in the preheated oven until tender, about 30 minutes.
Heat olive oil in a skillet over medium heat; cook and stir onion until softened, 5 to 10 minutes. Add garlic, cumin, salt, and black pepper to onion; cook and stir until fragrant, about 1 minute more.
Mix tomatoes, chicken broth, quinoa, and carrot into onion mixture; cook until quinoa is tender, about 12 minutes. Stir black beans and spinach into quinoa mixture, adding reserved tomato juice if mixture is dry. Spoon quinoa mixture into roasted red peppers and top with Mexican cheese blend.
Bake in the oven until cheese is melted, about 15 minutes.
