For the filling: Position a rack in the center of the oven and preheat the oven to 375 degrees F.
Stir together the sugar, flour and nutmeg in a medium saucepan. Gradually whisk in 1/4 cup water and the lemon juice to make a smooth mixture. Add the fruit and toss gently to coat evenly.
Put the saucepan on the stovetop over medium-low heat and stir the fruit mixture gently until it simmers. Reduce the heat to low and cook until thickened, about 2 minutes. Remove from the heat. Transfer to a shallow 2-quart baking or gratin dish and dot with the butter. Set aside.
For the biscuits: Stir together the flour, sugar, baking powder and 1/2 teaspoon salt in a large bowl. Work in the butter with your fingertips until the texture resembles coarse meal. Add the milk, vanilla and lemon zest to the dry ingredients and stir just until moistened to make a wet, slightly lumpy dough. Do not over mix.
Drop large spoonfuls of dough onto the top of the peaches, randomly spacing mounds of dough and leaving some uncovered areas to give a "cobbled" look. Spread the dough to an even thickness and sprinkle dough with sugar if desired.
Bake the cobbler until the biscuits are lightly browned, about 45 minutes. Let the cobbler set up at room temperature for 20 to 30 minutes before serving. Serve warm or at room temperature.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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