Preheat oven to 350°.
To prepare rice, heat 1 tablespoon oil in a Dutch oven over medium heat. Add mushrooms, green onion bottoms, ginger piece, and crushed garlic; cook 5 minutes, stirring frequently. Stir in rice, cumin, and chicken; cook 1 minute. Stir in broth; bring to a boil. Cover and bake at 350° for 25 minutes. Remove from oven; let stand, covered, for 10 minutes.
To prepare sauce, place cilantro and next 5 ingredients (cilantro through peeled garlic clove) in a food processor or blender; process until smooth. Stir into rice mixture. Discard ginger piece.
To prepare topping, heat 1 teaspoon oil in a medium skillet over medium-low heat. Add tomatoes; cook 2 minutes. Stir in 2 tablespoons green onion tops. Place rice mixture in a large bowl; spoon tomato topping over rice. Garnish with cilantro sprigs, if desired.