Preheat the oven to 400 degrees F. Butter a baking dish.
For the fruit: In a bowl, combine the peaches, sugar, flour, lemon juice and salt. Stir and set aside.
For the topping: In a separate bowl, combine the flour, sugar, baking powder and salt. Stir together. Add the butter and shortening, and then cut together with a pastry cutter. Beat the milk and eggs together. Pour into the flour mixture and stir with a fork until just combined.
Pour the peaches into the prepared baking dish. Tear off pinches of the dough topping and drop it onto the surface of the fruit, creating a "cobbled" texture. Sprinkle additional sugar over the top.
Bake until golden brown and bubbly, 30 to 35 minutes. Allow to sit for 10 to 15 minutes before serving. If the cobbler is too juicy, use a turkey baster to remove a little of the juice (or spoon the juice over ice cream). Serve warm with vanilla ice cream or fresh whipped cream.