Chef's Note: Like crisps, a cobbler needs no embellishments because the taste of fresh, ripe fruit is the point of this dessert. Use whatever fruit is in the height of its season. On the cusp of fall, for instance, I mix peaches with quince and will often add red bananas for their richness and subtle tropical flavor. Cut the extra dough into strips, roll up into spirals, and sprinkle or roll in cinnamon sugar as a treat for the kids.
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.