Combine first 6 ingredients, 1/8 teaspoon salt, and 1/8 teaspoon pepper in a medium bowl.
Sprinkle fish evenly with remaining 1/8 teaspoon salt and 1/8 teaspoon pepper.
Cut 2 (15-inch) squares of parchment paper. Fold each square in half, and open each.
Place half of vegetable mixture near each fold. Top each serving with 1 fillet, 1 teaspoon butter, and 2 tablespoons wine. Fold paper; seal the edges with narrow folds.
Place packets on a jelly-roll pan.
Bake at 350 for 18 minutes or until parchment is puffy.