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Make the biscuits: Position a rack in the upper third of the oven and preheat to 425ºF. Stack a rimmed baking sheet atop a second rimmed baking sheet and line with parchment paper (to prevent biscuit bottoms from burning).
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In a large bowl, combine the sweet rice, sorghum, oat, and tapioca flours with the ¼ cup sugar, baking powder, and salt. Add the butter and blend with a pastry cutter or your fingertips until the butter is the size of small peas. Chill until cold, 15 to 30 minutes.
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Meanwhile, in a measuring pitcher, whisk together the ½ cup cream, egg, and vanilla. Chill until needed.
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Gradually add the chilled cream mixture to the chilled flour mixture, then mix with a spoon until the dough holds together when you give it a squeeze. You may need to add 1 to 6 tablespoons of cream to properly hydrate the dough; the amount will vary depending on the temperature and humidity of your kitchen, and how much you’ve worked in the butter. Knead the dough in the bowl at least 20 times and then bring it together in a ball.
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On a surface dusted lightly with oat flour, pat the dough into a 1-inch high, even round. Use a 3-inch fluted cutter to cut rounds of dough and place them on the prepared baking sheet. Squash the dough scraps together, roll, and cut more rounds, repeating until you’ve used all the dough. Chill until firm, 20 minutes.
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Brush the tops of the biscuits with the remaining 1 tablespoon heavy cream and sprinkle with the remaining 2 teaspoons sugar. Bake until the tops are golden, and the biscuits are cooked through, 20 to 25 minutes. Let cool to warm or room temperature.
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Meanwhile, make the whipped crème fraîche: Combine the heavy cream, crème fraîche, sugar, and vanilla in the bowl of a stand mixer fitted with the whip and beat on medium-high until the mixture just holds soft peaks. Cover and chill until needed.
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Prepare the berries: A half hour before serving, toss together the berries, sugar, lemon or lime juice, and salt. Let sit at room temperature to draw out the juices, at least 10 minutes or up to two hours.
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To serve, carefully slice the biscuits in half (a small serrated knife works well) and place the bottoms on plates. Top each with a generous dollop of whipped crème fraîche, a mound of berries and their juice, and the top biscuit. Serve immediately.