In a large bowl, combine the sliced peaches, 0.75 cup sugar, 2 tablespoons flour, cinnamon, and nutmeg. Toss gently to coat the peaches evenly.
Pour the peach mixture into a 9x13 inch baking dish. Dot the top with the 2 tablespoons of butter pieces.
In a separate bowl, whisk together 1.5 cups flour, 0.33 cup sugar, baking powder, and salt.
Cut in the 0.5 cup cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Gradually add the milk, stirring just until a soft dough forms. Do not overmix.
Drop spoonfuls of the biscuit dough over the peach mixture, leaving some gaps for steam to escape.
Bake for 35-45 minutes, or until the topping is golden brown and the peach filling is bubbly.
Let cool slightly before serving. Serve warm, perhaps with a scoop of vanilla ice cream.
Notes
For a sweeter cobbler, increase the sugar in the filling slightly. If using frozen peaches, do not thaw them completely, and you may need to increase baking time slightly.