Shell fava beans; cook in boiling water to cover 1 minute. Drain well. Rinse under cold running water, and pat dry. Use your fingertips to pull a bit of the tough skin from the top of each bean, and push bean out of skin. Set beans aside.
Melt 1 tablespoon butter over medium heat in a medium skillet; add mushrooms, 1/4 teaspoon salt, and pepper. Sauté 4 minutes or just until tender. Transfer to a plate.
Add 1 tablespoon butter to the skillet. Add onion and remaining 1/4 teaspoon salt; sauté 2 minutes. Add corn and remaining 1 tablespoon butter, and sauté 3 minutes. Stir in fava beans, and sauté 2 minutes. Add mushrooms; sauté 1 minute or until thoroughly heated. Stir in tarragon, and serve immediately.