To prepare the cheese sauce, add the cubed potatoes and sliced carrots to a pot of water. Bring to a boil and boil uncovered until tender, about 18-20 minutes.
Meanwhile, cook 2 cups of dried rice according to package directions and set aside.
Lightly saute the broccoli. Add a splash of water to a pot over low-medium heat. Add the broccoli and lightly saute with the lid on until the broccoli is bright green and tender, about 5-6 minutes. Remove from the heat, drain any remaining water, and set aside.
After the potatoes and carrots are finished cooking, reserve 2 cups of cooking water before draining. Drain the remaining water and add the drained potatoes and carrots to a high-speed blender. Add the nutritional yeast, soaked cashews, garlic powder, onion powder, salt, pepper, and reserved water to the blender. Blend on high until completely smooth. Set aside.
Combine the rice, broccoli, optional chili flakes, and prepared cheese sauce to a large pot. Stir until well combined. Serve in a baking dish immediately or broil for 3-5 minutes until bubbling and lightly golden.