Preheat the broiler. Whisk the salsa, sour cream and 3/4 cup water in a bowl.
Heat the olive oil in a large ovenproof nonstick skillet over medium-high heat. Add the broccoli, bell pepper, scallion whites and garlic; season with salt and pepper. Cook, stirring, until softened, about 6 minutes. Add the cumin and stir until toasted, 30 seconds.
Stir in the chicken, rice, salsa mixture and 1 teaspoon salt. Bring to a boil, then reduce the heat to medium and simmer until heated through and saucy, 1 to 3 minutes. Fold in half of the cheese; top with the rest. Broil until the cheese melts, 2 to 4 minutes. Top with the scallion greens.