Preheat your oven to 350°.
Place the carrots, cauliflower, onion, and cashews in a large pot. Fill it with enough water to cover the vegetables plus about two inches.
Bring the water to a boil over medium-high heat and then reduce the heat and allow to simmer for about 15 minutes, or until the vegetables are fork tender.
Drain the vegetables and save the water. Allow the vegetables to cool slightly and then place them in a high-speed blender or food processor along with the nutritional yeast, lemon juice, garlic, mustard, cornstarch, and salt. Add 2 cups of the reserved cooking water and blend until smooth and creamy.
While the vegetables are cooking, steam the broccoli. Add about an inch of water to a large pot. Place a steamer basket inside and fill it with the broccoli florets. Bring the water to a boil, cover the pot, and let cook for about 3 minutes.
If you don’t have a steamer basket, you can blanch the broccoli. Bring a large pot of salted water to boil, and have a bowl of ice water standing by. Cook the broccoli in the water for a minute or two. Remove the broccoli with a slotted spoon and plunge into immediately in the ice water.
In a large bowl, mix together the cooked brown rice, steamed broccoli, and cheese sauce. Pour the mixture into a large casserole dish. Sprinkle the top with paprika.
Bake your casserole for 30 minutes or until the cheese is bubbly and the top has turned golden brown.