Preheat oven to 375°.
Cook first 3 ingredients in a large nonstick skillet over medium-high heat until meat is browned, stirring to crumble. Add water and next 6 ingredients (water through chiles); bring to a boil. Cover, reduce heat, and simmer 10 minutes. Uncover and simmer an additional 2 minutes. Remove from heat; set aside.
Combine the rice, sour cream, sliced green onions, and milk in a bowl. Spoon rice mixture into a 9-inch baking dish. Top with beef mixture; sprinkle with cheese. Bake at 375° for 10 minutes or until thoroughly heated. Let stand 5 minutes before serving.
Note: The beef mixture could also be used as a filling for burritos.