Combine water and broth in a medium saucepan; bring to a simmer (do not boil). Keep broth mixture warm over low heat.
Heat oil in a large saucepan over medium-high heat. Add rice, cumin, coriander (if desired), and garlic; sauté 1 minute. Stir in 1/2 cup broth mixture; cook 2 minutes or until the liquid is nearly absorbed, stirring constantly. Add remaining broth mixture, 1/2 cup at a time, stirring constantly until each portion of liquid is absorbed before adding the next (about 20 minutes total). Stir in the onions, cheese, hot sauce, corn, and bell peppers; cook 3 minutes or until thoroughly heated.