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1
Heat the oven to 425 degrees F and arrange a rack in the middle.
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2
Place the brown sugar, lemon juice, cornstarch, vanilla, and salt in a large bowl and whisk to combine.
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3
Add the peaches and stir until evenly coated.
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4
Transfer the mixture to an 8-by-8-inch glass or ceramic baking dish, arrange in an even layer, and scatter the butter pieces over the top.
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5
Bake until the peaches are starting to soften and release their juices, about 15 to 20 minutes.
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6
Meanwhile, make the topping.
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7
Whisk together the flour, 3 tablespoons of the sugar, the baking powder, and baking soda in a large bowl to combine.
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8
Add the butter and toss with your fingers until well coated in the flour mixture.
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9
Using a pastry blender or 2 knives, cut the butter into the dry ingredients until reduced to pea-size pieces, about 2 to 3 minutes.
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10
Add the buttermilk or yogurt and stir until a soft, crumbly dough forms.
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11
Divide the dough into 9 equal portions.
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12
Form each portion into a 2-inch-wide patty and place on a large plate.
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13
Cover with plastic wrap and set aside.
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14
When the peaches are ready, remove the baking dish from the oven, stir to coat the peaches in the juices, and arrange in an even layer again.
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15
Place the dough patties in a single layer on top.
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16
Sprinkle the remaining tablespoon of sugar evenly over the top of the cobbler.
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17
Bake until the biscuits are golden brown and the filling is bubbling around the edges, about 15 minutes.
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18
Transfer to a wire rack and let cool for at least 20 minutes before serving.
