Preheat oven to 350°F and grease a donut pan.
In a saucepan over medium heat, combine peaches, brown sugar, cinnamon, and cornstarch. Cook until slightly thickened, then cool completely.
In a bowl, beat cream cheese, powdered sugar, and vanilla until smooth. Refrigerate until ready to use.
In another bowl, combine flour, brown sugar, cinnamon, and cold butter until crumbly. Bake crumble topping for 10 minutes until lightly golden.
In a large bowl, whisk flour, sugar, baking powder, cinnamon, and salt.
In another bowl, whisk milk, egg, melted butter, and vanilla extract.
Combine wet and dry ingredients until just mixed.
Fill donut pan about 3/4 full and bake for 10–12 minutes until lightly golden. Cool completely.
Pipe or spread cheesecake filling onto donuts.
Top with peach filling and crumble topping before serving.