1cupbrown ricecooked according to package instructions (when cooked, it should be between 3 and 4 cups)
¼cuppanko bread crumbs
Preheat oven to 350ºF.
Bring an inch of water to a boil in a medium saucepan fitted with a steamer basket. Place the broccoli and carrots in the basket, cover, and steam for 3-5 minutes, or until tender. Transfer the veggies to a large bowl, then drain and dry the saucepan.
Return the saucepan to medium-low heat. Once the saucepan is warm, add the butter and let it melt, then stir in the onions and garlic. Cook for about 7 minutes, or until the onions are softened and translucent. Sprinkle the flour over the onions and cook 2-3 minutes more, stirring constantly, until flour is golden brown. Slowly pour the milk into the saucepan, whisking to incorporate it into the flour as you pour. Take your time with this step! Once all the milk is in the saucepan, bring the mixture to a simmer, continuing to whisk constantly. Continue to cook, whisking often, until the sauce is thickened and coats the back of a wooden spoon (about 5 minutes more). Remove from heat and whisk in 1 cup of the cheddar cheese, the parmesan cheese, mustard powder, and paprika. Season to taste with salt and pepper.
Transfer the cooked rice to the bowl with the broccoli and carrots and pour the cheese sauce on top. Stir to incorporate; taste and add additional salt and pepper, if needed. Grease a square baking dish with butter or spray it with an oil mister (or cooking spray, if you don't have an oil mister); transfer the rice mixture to the baking dish and top with the remaining ¼ cup of cheddar cheese and the panko. Spray the top of the casserole with additional oil and bake for 25 minutes, then broil for about 3 minutes more, until the panko is lightly browned. Remove from oven and let the casserole sit for about 5 minutes before serving.
Cheese sauce can be temperamental, so while I usually encourage substitutions and experimentation with recipes, it's best to follow this one to the letter so your sauce doesn't separate. Whole milk makes a more stable sauce, but I have successfully made cheese sauces with reduced-fat milk too. If at all possible, use cheese that you've shredded yourself—bagged shredded cheese contains anti-caking agents that can affect the texture of cheese sauces.