Make the peach filling: In a small saucepan, combine chopped peaches, brown sugar, cinnamon, cornstarch, and water. Cook over medium heat, stirring constantly, until the mixture thickens and the peaches soften (about 5–7 minutes). Remove from heat and let cool completely.
Prepare the cheesecake filling: In a mixing bowl, beat the softened cream cheese, powdered sugar, and vanilla until smooth. Gradually add the heavy cream and continue beating until light and fluffy. Cover and refrigerate until ready to use.
Fry the donuts: Heat vegetable oil in a deep pot or fryer to 350°F (175°C). Open the biscuit can and gently separate the rounds. Use a small round cutter or bottle cap to cut a hole in the center of each biscuit to form a donut shape. Fry 2–3 donuts at a time for 2–3 minutes per side, or until golden brown. Drain on paper towels and let cool slightly.
Assemble: Once donuts are cool enough to handle, slice them horizontally like sandwich buns. Spread a layer of cheesecake filling on the bottom half, then spoon a generous portion of cooled peach filling on top.
Finish and serve: Place the top half of the donut back on, then drizzle with glaze, sprinkle with crushed graham crackers, and dust lightly with cinnamon. Serve slightly warm or at room temperature.