In a medium bowl, soak rice in warm water for 10 minutes. Drain in a fine-mesh sieve, then rinse rice in sieve under running water until water mostly runs clear.
Meanwhile, arrange a rack in center of oven; preheat to 375°. In a large skillet over medium heat, cook chorizo, stirring occasionally, until no longer pink, about 7 minutes. Using a slotted spoon, transfer to a 13" x 9" baking dish.
In same skillet over medium heat, add onion; season with ½ tsp. salt. Cook, stirring occasionally, until starting to soften, about 5 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more. Stir in beans; season with remaining ¼ tsp. salt. Using a slotted spoon, transfer to baking dish. Add rice, broth, salsa, and taco seasoning to baking dish and stir to combine. Cover dish with foil.
Bake burrito rice, stirring halfway through, until rice is tender, about 45-50 minutes.
Turn on broiler. Remove foil and top rice mixture with cheddar and queso.
Broil, watching closely, until cheese is brown and bubbly, 2 to 3 minutes.
Top with tomatoes and cilantro. Serve with sour cream and tortillas alongside.
