01 - In a bowl, combine flour, brown sugar, cinnamon, and salt. Mix in melted butter until coarse crumbs form. Set aside for later use.
02 - Combine peaches, brown sugar, lemon juice, and cornstarch in a small saucepan over medium heat. Stir frequently for 3–5 minutes until thickened. Allow to cool completely.
03 - Beat cream cheese until smooth. Add sugar and vanilla, continuing to beat until creamy. Transfer mixture to a piping bag and refrigerate until needed.
04 - Whisk flour, sugar, baking powder, baking soda, and salt in a large bowl. In a separate bowl, whisk milk, melted butter, eggs, vanilla, and sour cream. Pour wet ingredients into dry ingredients and stir until just combined, avoiding overmixing.
05 - Heat oil to 350°F. Scoop batter into greased donut molds or pipe rings onto parchment squares. Fry for 2–3 minutes per side until golden brown. Drain on paper towels and let cool slightly.
06 - Create a cavity in each donut using a knife or piping tip. Pipe cheesecake filling into the center, then add a spoonful of the cooled peach filling.
07 - Whisk powdered sugar and milk until smooth. Dip the top of each donut into the glaze.
08 - Sprinkle the prepared cobbler crumb topping generously over the glazed donuts. Allow the glaze to set before serving.