Combine 1/4 cup broth and flour in a small bowl, stirring with a whisk until smooth. Add remaining broth, garlic, and thyme; set aside.
Place a large nonstick skillet coated with cooking spray over medium-high heat until hot. Add chicken, and cook 4 to 5 minutes or until lightly browned. Turn chicken; add 2 tablespoons green onions. Pour broth mixture over chicken; sprinkle with salt and pepper. Reduce heat, and simmer, uncovered, 15 to 20 minutes or until chicken is done, basting often.
Remove chicken from pan; keep warm. Bring sauce to a boil over medium-high heat. Scrape bottom and sides of pan, using a rubber spatula. Cook 2 minutes or until sauce is reduced to 3/4 cup. Pour sauce evenly over chicken, and top with remaining green onions.