Preheat oven to 400 degrees Fahrenheit. Cook the quinoa: Rinse and dry quinoa. Combine 1 cup quinoa and 1 ¾ cup water in a medium saucepot and bring to a boil. Cover and reduce heat to medium-low; simmer for about 15 minutes or until the water is absorbed. Fluff with a fork.
While the quinoa is cooking, saute the veggies. In a medium pan or skillet, heat olive oil on medium heat. Add chopped onion and cook for 1-2 minutes. Add Brussels sprouts and cook for 3 minutes. Then add mushrooms, kale, and garlic and cook for another 3 minutes. Season with salt, red chili flakes, and lemon juice.
Combine the quinoa and veggies in a large bowl and mix in the Gouda and ¼ cup Pecorino Romano cheese (save ¼ cup Pecorino Romano cheese for the next step).
Place the mixture in a ceramic 8x8 baking dish. Top with the remaining cheese.
Bake in the oven for 15-20 minutes. Serve immediately.
You can store the quinoa bake in an airtight container and consume within 4-5 days.