Combine first 3 ingredients in a small bowl; stir together cornstarch and 1/3 cup water, and add to soy sauce mixture.
Stir-fry half of steak in 1 Tbsp. hot olive oil in a large wok or skillet over high heat 3 to 4 minutes or to desired degree of doneness. Transfer steak to a plate; repeat procedure with 1 Tbsp. olive oil and remaining steak.
Stir-fry bell pepper, next 3 ingredients, and half of green onions in remaining 1 Tbsp. hot olive oil 2 to 3 minutes or until tender. Add soy sauce mixture and steak; bring to a boil, stirring constantly; cook, stirring occasionally, 1 minute or until sauce is slightly thickened. Remove from heat, and sprinkle with remaining green onions. Serve immediately over hot cooked rice.