Start by peeling and slicing the peaches. You should have about 6 cups of sliced peaches. In a large bowl, combine the peaches, granulated sugar, brown sugar, cinnamon, nutmeg, vanilla extract, and lemon juice. Mix well and set aside.

In a separate bowl, combine the flour, baking powder, and salt. Add the cold cubed butter and vegetable oil. Use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs. Gradually add the milk, stirring until the dough comes together.

Preheat your oven to 375°F (190°C). Pour the peach mixture into a greased 9x13-inch baking dish. Drop spoonfuls of the dough evenly over the peach mixture. Don't worry about covering the peaches completely; the dough will spread as it bakes.

Bake in the preheated oven for 35-40 minutes, or until the crust is golden brown and the peach filling is bubbly. Allow the cobbler to cool for a few minutes before serving.