Heat oven to 350°F and grease a 9x13-inch baking dish.
Melt butter in a skillet over medium heat. Soften onion until translucent, about 5 minutes.
Stir in garlic and cumin. Cook until fragrant, 30 seconds. Remove from heat.
Whisk sour cream, cream cheese, broth, and lime juice in a large bowl until smooth.
Fold in cooked rice, green chiles, sautéed onions, salt, pepper, and half of each cheese.
Spread mixture in the dish. Top with remaining cheeses.
Bake until hot and bubbling with lightly browned spots, 30–35 minutes.
Rest 10 minutes. Sprinkle with cilantro and serve warm.
Notes
For a heartier version, stir in a cup of cooked shredded chicken or crumbled cooked chorizo. Want extra heat? Swap part of the mild chiles for hot green chiles or add a pinch of chili powder. Leftovers keep well refrigerated up to 4 days; reheat covered at 325°F until warmed through.This recipe is an original creation inspired by classic Cheesy Green Chile Rice Casserole Recipe flavors. All ingredient ratios and instructions are independently developed.