In 2-quart saucepan, heat 2 inches of water to boiling. Add corn; reduce heat. Simmer uncovered 5 minutes; drain. Rinse with cold water; drain and set aside.
In 10-inch skillet, heat butter and oil over medium-high heat until butter is melted. Add onion; cook 2 to 3 minutes, stirring frequently, until crisp-tender.
Stir in edamame and broth. Heat to boiling; reduce heat. Simmer uncovered about 10 minutes, stirring occasionally, until edamame are tender.
Stir in corn and salt. Cook 4 to 6 minutes, stirring occasionally, until corn is hot. Sprinkle with basil just before serving.