In a medium saucepan, melt 2 tablespoons butter over medium-low heat. Add onion; cover, and cook for 20 minutes, stirring occasionally. Remove cover, and raise heat to medium-high; cook for 8 to 10 minutes, stirring frequently. Add vinegar, salt, and pepper. Cook for 1 to 2 minutes, or until vinegar evaporates. Let onion cool completely; finely chop.

In a small bowl, combine remaining ¾ cup butter, onion, and tarragon. Beat at medium-high speed with an electric mixer until combined. Refrigerate for 15 minutes.

Place butter on a large piece of parchment paper. Roll into an 8x2-inch log, twisting parchment at ends. Refrigerate for at least 1 hour. Slice into ¼-inch slices. Store in refrigerator for up to 1 week.