Preheat oven to 350 degrees F.
In a large bowl, combine peaches, tapioca, sugar, and salt. Gently mix in berries and vinegar. Taste for balance and add more vinegar, if desired. Spoon mixture into an 8 by 8-inch baking dish.
In a large mixing bowl, combine flour, salt, 3 tablespoons brown sugar, and baking powder. Work in the butter using your fingers or a pastry cutter until the mixture forms large pea sized lumps. This can also be done with the paddle attachment of a stand mixer, or with brief pulses in a food processor. Slowly mix in 3/4 cup heavy cream until just combined.
Gather dough together into a ball and knead gently on a lightly floured board until it holds together. Roll out to 1/2-inch thickness. Using a 3-inch round or star cutter, cut dough into shapes. Place them decoratively on the fruit mixture. Brush pastry with 1 tablespoon of cream and then sprinkle with remaining 1 tablespoon brown sugar. Bake until pastry is golden brown and the fruit is bubbly, about 40 minutes. Put cobbler under broiler for a few seconds to brown pastry, if necessary.
Beat remaining 1 cup of cream in a medium bowl with a whisk or electric mixer on high. Gradually beat in 1/4 cup granulated sugar. Beat until it holds soft peaks, and then add the vanilla. Serve with cobbler.
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