In a medium saucepan, bring two cups of vegetable broth to a boil. Add one cup of rinsed quinoa; reduce heat, cover, and let simmer for about twelve to fifteen minutes until all the liquid is absorbed. Fluff with a fork and set aside.
In a large skillet, heat one tablespoon of olive oil over medium heat. Add diced onion and minced garlic; cook until fragrant (about two minutes). Stir in bell pepper, zucchini, mushrooms, and cherry tomatoes; cook for five to seven minutes until softened. Add baby spinach, season with oregano, basil, smoked paprika, salt, and pepper, stir until spinach wilts, then remove from heat.
In a small bowl, mix tomato sauce, Greek yogurt, and red pepper flakes (if using). Stir until well combined.
Preheat oven to 190 degrees Celsius (375 degrees Fahrenheit). In a large mixing bowl, combine cooked quinoa, sautéed vegetables, and sauce; stir until everything is evenly coated, then transfer mixture to a lightly greased baking dish (9x13 inches).
Sprinkle mozzarella cheese and Parmesan cheese evenly over the top; cover with foil, bake for twenty minutes, then remove foil and bake for another ten minutes until cheese is bubbly and slightly golden.
Let casserole rest for five minutes before serving; garnish with chopped fresh parsley or basil, then enjoy!