Heat the oven to 375°F and arrange a rack in the middle.
For the biscuits:
- Combine flour, brown sugar, baking powder, baking soda, and salt in a mixing bowl and whisk to aerate and break up any lumps.
- Using the large holes of a box grater, grate frozen butter into flour mixture and toss to coat. Smear in sour cream and heavy cream and, using your hands, knead until dough just comes together. Divide into six pieces and flatten into disks; cover and reserve in the refrigerator.
For the filling:
- Mix together flour, brown sugar, granulated sugar, salt, and vanilla seeds. Add peaches and blackberries and mix until fruit is evenly coated.
- Turn fruit into a 2-quart baking dish and stagger reserved biscuit dough evenly across the top.
To assemble:
- Brush tops of biscuits with sour cream and sprinkle with sugar.
- Bake until filling bubbles, peaches are tender when pierced with a knife, and biscuits are golden brown and cooked through, about 30 to 35 minutes. Let cool at least 5 minutes before serving.
Beverage pairing: Saracco Moscato d’Asti, Italy. Sprightly and buoyant on the palate, Moscato d’Asti, a sparkling sweet wine from northern Italy, is a refreshing match for this cobbler. Light carbonation and texture make it a welcome contrast for the richness of the cobbler, while its flavors of pear, peach, and spice accent the fruit.
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