Combine first 5 ingredients in a bowl, stirring well with a whisk. Set aside.
Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add 1/4 cup chopped green onions, ginger, and garlic to pan; sauté 30 seconds. Add beef to pan, and sauté for 4 minutes or until browned. Remove from pan.
Wipe pan dry with a paper towel. Add remaining 1 teaspoon oil to pan; heat over medium-high heat. Add beans and pepper to pan. Cover and cook 3 minutes. Uncover and cook 3 minutes, stirring frequently. Add 3/4 cup green onion tops; sauté 1 minute. Return beef mixture to pan. Stir in broth mixture; bring to a boil. Cook 1 minute, stirring constantly. Remove from heat. Serve with rice.