Preheat your oven to 375°F (190°C). Butter a 9x13 inch baking dish or a similar-sized oven-safe skillet.

Prepare the peach filling: In a large bowl, gently toss the sliced peaches with granulated sugar, cornstarch, cinnamon, nutmeg, and lemon juice until evenly coated. Pour the peach mixture into the prepared baking dish.

Make the cream cheese biscuit topping: In a separate bowl, whisk together the flour, sugar, baking powder, and salt. Cut in the cold cream cheese and cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces.

Gradually add the milk, stirring just until the dough comes together. Be careful not to overmix. The dough should be slightly sticky.

Drop spoonfuls of the biscuit dough evenly over the peach filling. Don't worry about covering the entire surface; gaps are good for steam to escape.

Brush the tops of the biscuits with the extra tablespoon of milk and sprinkle with turbinado sugar for a golden-brown crust.

Bake for 40-50 minutes, or until the topping is golden brown and the peach filling is bubbly and thickened. If the topping starts to brown too quickly, you can loosely tent the dish with foil.

Let the cobbler cool for at least 15-20 minutes before serving. Serve warm, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream.