1. Preheat oven to 400°.
2. Combine first 3 ingredients, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a large bowl. Add mushrooms; toss gently to coat. Arrange mushrooms, cap sides down, on a jelly-roll pan. Bake at 400° for 12 minutes or until tender. Remove from oven. Place 1 mushroom on each of 4 plates. Add wine, stock, and mustard to jelly-roll pan; stir with a whisk to mix with mushroom juices. Pour wine mixture into a small saucepan over medium heat. Bring to a boil; cook until wine mixture is reduced to 1/4 cup (about 15 minutes). Combine 1 teaspoon water and cornstarch, stirring with a whisk. Stir cornstarch mixture into wine mixture; boil 1 minute or until mixture begins to thicken, stirring constantly with a whisk. Remove from heat. Add vegan butter and tarragon, stirring until butter melts.
3. Heat canola oil in a large skillet over medium-high heat. Add potato wedges; cook 3 minutes on each side or until the wedges are browned. Sprinkle with remaining salt and pepper and serve with mushrooms and wine sauce.