1. Combine 1/4 cup green onions, cilantro leaves, 1/4 teaspoon salt, 1/8 teaspoon pepper, 1/2 cup broth, chile, and 1 garlic clove in a food processor; process until blended.
2. Heat 1 tablespoon oil in a large skillet over medium-high heat. Add 1/4 cup onions, mushrooms, and remaining garlic clove to pan; sauté 2 minutes. Add cilantro mixture, remaining 1 1/4 cups broth, rice, 1/2 cup water, and cumin to pan; bring to a boil. Cover, reduce heat, and simmer 25 minutes or until liquid is absorbed. Remove from heat; cover and let stand 5 minutes. Add parsley to rice mixture; fluff with a fork.
3. Heat remaining 1 tablespoon oil and butter in a large skillet over medium-high heat. Sprinkle chicken with the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Add chicken to pan; cook 5 minutes on each side or until done. Remove chicken from pan; cut each chicken piece crosswise into 1/2-inch slices.
4. Heat 1 teaspoon olive oil in a small saucepan over medium-high heat. Add remaining 1/4 cup onions and tomatoes; sauté 2 minutes. Arrange 1 cup rice mixture on each of 4 plates; top each serving with 1 breast half and 2 tablespoons tomato mixture. Garnish with cilantro sprigs, if desired.