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Preheat your oven to 425°F. Lightly butter or grease a 9" x 13" pan.
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In a medium bowl, combine the fruit, melted butter, and lemon juice, tossing to coat the fruit.
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In a separate small bowl, whisk together the sugar and thickener, then sprinkle over the fruit.
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Toss gently with a spatula until the fruit is coated, then scoop the fruit into the pan. Pat the inside of the bowl with a clean towel so it's mostly dry.
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In the same mixing bowl, whisk together the flour(s), sugar, baking powder, and salt. In a separate bowl or a liquid measuring cup, whisk together the melted butter, milk, egg, and almond extract. Pour the wet ingredients into the dry and mix just until thoroughly combined.
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Dollop the biscuit topping in blobs atop the fruit (3 across and 4 down in a 9" x 13" pan), leaving 1/2" or so between them. Fill in the in-between spaces with any leftover dough. Sprinkle with sugar.
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Bake the cobbler for 20 minutes. Reduce the oven temperature to 375°F, and bake for an additional 25 minutes, until the biscuits are golden and the filling is bubbly. (Be sure to bake until the biscuits are a deep golden brown, otherwise the biscuits in the center may be under-baked.) Remove the cobbler from the oven and let it cool slightly before serving warm or at room temperature.
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Store leftover peach cobbler, covered, in the refrigerator for up to 5 days.