Preheat your oven to 350°F (175°C) and lightly grease a donut pan to prevent sticking.
In a large bowl, whisk together the flour, sugar, baking powder, and salt. In a separate bowl, mix the milk, egg, vanilla, and melted butter. Combine wet and dry ingredients until just mixed.
Spoon the batter into each donut mold, filling them about three-quarters of the way full. Bake for 12-15 minutes or until a toothpick comes out clean. Allow to cool.
Beat the cream cheese, powdered sugar, and vanilla until the mixture is smooth. Transfer to a piping bag.
Combine peaches, brown sugar, cinnamon, and cornstarch in a small saucepan. Cook over medium heat until thickened and jammy (about 5 minutes). Let cool.
Mix graham cracker crumbs, sugar, melted butter, and cinnamon until crumbly.
Pipe cheesecake filling into the center of each donut. Spoon the peach topping over each donut, then sprinkle generously with cobbler crumble.
