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Combine the flour, brown sugar, baking powder, and the salt in a mixing bowl. You may need to work the brown sugar into the flour a bit to get all the lumps out.
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Using a pastry blender or a knife and fork, cut the cold butter into the flour mixture. You want to still have pea-sized chunks of butter, do not overwork it, and err on the bigger lumps.
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In a measuring cup, stir together the cream and the sourdough starter.
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Quickly and gently, barely mix in the sourdough starter mixture into the butter/flour. Do not over mix. You will mix it in a bit more when you knead and roll it out.
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Scrape out the mixed barley dough onto a clean work surface.
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Knead the dough briefly, trying not to work the dough very much. But knead until it comes together. Use a gentle hand.
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Roll or pat the dough out to ¾ inch thickness.
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Cut with a 3-inch round cutter or a glass into as many circles as possible. Gather together and repeat out and cut until you have no more dough. Be gentle and try not to work the dough very much. Rough is fine.
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Arrange the cut circles just barely touching on top of the apricot topping.
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Sprinkle generously more sugar, or coarse sugar if you have it, over the top of the sourdough topping.
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Bake for 40-45 minutes or until the topping is golden brown and the filling is bubbling nicely.