Sprinkle 1/8 teaspoon salt over the fillets. Melt 1 1/2 teaspoons butter in a large nonstick skillet over medium-high heat. Add fillets, and sauté 4 minutes on each side or until fish flakes easily when tested with a fork. Remove fillets from skillet, and keep warm.
Melt 1 1/2 teaspoons butter in skillet. Add 1/8 teaspoon salt, mushroom slices, and pepper; sauté for 4 minutes or until golden. Add sherry, and cook for 30 seconds, stirring constantly.
Combine broth, milk, and cornstarch, and stir with a whisk. Add broth mixture to skillet, and bring to a boil, stirring constantly. Reduce heat to medium, and cook 1 minute. Spoon sauce over fish.