Melt one tablespoon of butter over medium-low heat in a medium-sized skillet. Add the shallots and cook, stirring frequently until the shallots are translucent. About 2 minutes. Do not allow the butter or the shallots to caramelize.
Add the wine, vinegar, and water. Turn the heat up to medium, stirring occasionally, until the liquid has cooked off, about 4 minutes. Remove from heat immediately and allow to cool completely.
In a mixing bowl, add the remaining butter, the cooled shallots, and the tarragon. Using a silicone spatula, mix thoroughly until the butter is completely seasoned with the ingredients and everything is evenly distributed. There should be no streaks of unseasoned butter.
Shape the butter into a ball, scraping the sides of the mixing bowl clean, and scoop it onto the center of an approximately 10-inch section of plastic wrap. With your hands outside the plastic wrap, gently pack the 4 sides of the butter mass to shape into a small brick.
Completely wrap the butter in the plastic wrap until it is somewhat tube shaped. Then, holding the plastic on both ends of the tube, spin the wrapped butter until the tube is more compact and is sealed by the twisted ends of plastic.
Refrigerate for 30 minutes or until firm.
Serve slices of the compound butter over steaks, fish, or use to season other dishes such as pasta or rice.