Rinse and core tomatoes; cut into chunks. Whirl in a blender or food processor until smooth, then rub through a fine strainer into a bowl; you should have about 3 cups. Discard residue. Season purée to taste with 2 to 3 tablespoons vinegar and salt. Cover and chill until cold, at least 1 hour.
Peel and pit avocados; cut into chunks. In a blender or food processor, whirl avocados, broth, sour cream, and lime juice until smooth. Add salt to taste. Cover surface with plastic wrap and chill until cold, at least 1 hour.
Peel cucumber; cut in half lengthwise and scoop out and discard seeds. Dice cucumber into 1/8-inch pieces; you should have about 1 cup. In a small bowl, mix cucumber, shallots, 1 tablespoon vinegar, and minced tarragon. Cover and chill until cold, at least 30 minutes.
To serve, stir avocado mixture to blend and pour equal portions into glasses (12 to 16 oz. each). Whisk tomato mixture to blend and gently pour over avocado. Top with diced-cucumber mixture. Clear, straight-sided glasses or wineglasses show off the layers of color best, but large martini glasses also work. You can also use soup bowls and keep the layers a surprise.