Sprinkle 1/8 teaspoon salt and pepper over fish. Melt 1 1/2 teaspoons butter in a large nonstick skillet over medium-high heat. Add fish, and cook 7 minutes on each side or until fish flakes easily when tested with a fork. Remove from skillet, and keep warm.
Melt 1 1/2 teaspoons butter in skillet over medium heat. Add the shallots, and sauté for 1 minute or until tender. Add wine, and cook for 30 seconds. Combine 1/8 teaspoon salt, broth, Dijon mustard, and cornstarch, and stir with a whisk. Add to skillet, and bring to a boil. Reduce heat, and simmer until reduced to 3/4 cup (about 1 minute). Spoon sauce over fish, and sprinkle with tarragon.