Step 1: Prepare the Peach Cobbler Filling. In a small saucepan, combine the chopped peaches, brown sugar, cinnamon, cornstarch, and lemon juice. Cook over medium heat, stirring frequently, until the mixture thickens and peaches are tender, about 5-7 minutes. Remove from heat and let cool completely. This can be made ahead of time.
Step 2: Preheat your oven to 350°F (175°C) and lightly grease a 12-cavity donut pan.
Step 3: Prepare the Donut Batter. In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, and salt.
Step 4: In a separate medium bowl, whisk together the egg, milk, melted butter, and vanilla extract.
Step 5: Pour the wet ingredients into the dry ingredients and mix with a spatula until just combined. Be careful not to overmix; a few lumps are okay.
Step 6: Fill the Donut Pan. Spoon or pipe about 1 tablespoon of batter into each donut cavity. Then, spoon about 1-2 teaspoons of the cooled peach filling onto the center of the batter in each cavity. Top with another tablespoon of donut batter, spreading it gently to cover the peach filling. This is where a quality chef's knife comes in handy for finely dicing those peaches!
Step 7: Bake the donuts for 12-15 minutes, or until golden brown and a toothpick inserted into a donut comes out clean (avoiding the peach filling). Let cool in the pan for 5 minutes before transferring to a wire rack to cool completely.
Step 8: While the donuts cool, prepare the Cheesecake Glaze. In a medium bowl, beat the softened cream cheese and softened butter with an electric mixer until smooth and creamy.
Step 9: Gradually add the sifted powdered sugar, beating until fully incorporated. Add the milk/cream one tablespoon at a time until the glaze reaches your desired consistency. Stir in the vanilla extract.
Step 10: Once the donuts are completely cool, dip the top of each donut into the cheesecake glaze. You can also drizzle extra peach filling or fresh peach slices on top for garnish, if desired. Serve immediately and enjoy!