Combine the peaches, sugar, cinnamon, lemon juice, and salt in a pot. Cook over medium heat until the peaches are juicy and starting to thicken, about 15-20 minutes. Mash them until the peaches are small and jammy. Then stir in the cornstarch slurry and cook 2 minutes longer. Transfer the jam to a clean bowl and set aside to cool.
Cream the butter, cream cheese, sugar, and brown sugar until light and fluffy.
Mix in the egg, egg yolk, and vanilla extract.
Mix in the flour, baking powder, and salt until just combined.
Chill the dough in the fridge for 30 minutes to firm and make it easier to scoop.
In a small bowl, combine the sugar and cinnamon. Scoop the dough into 2 tbsp-sized balls directly into the bowl of cinnamon sugar, tossing to coat them. Then place them on a parchment-lined tray with 1-2 inches of space in between each one.
Use the back of a round measuring spoon to indent the center of the cookie dough balls. Then fill the center with a heaping teaspoon of peach cobbler filling. Chill the tray in the freezer for a minimum of 3-4 hours, overnight is best!
Preheat the oven to 350 F/180 C.
Make the cinnamon crumb topping. Combine the crumb ingredients until crumbs form. Bake the crumbs on a parchment-lined baking sheet for 12-15 minutes, or until golden brown. Set it aside to cool, then break it into small crumb pieces.
Press a handful of the cinnamon crumbs on top of each cookie. Bake them spaced 2-3 inches apart for 12-13 minutes.
Pull the tray out of the oven and sprinkle them with more of the cinnamon crumb. Let the tray cool on a wire rack until completely cool before removing. While they cool, make the vanilla glaze.
Whisk together the powdered sugar, milk, and vanilla extract until smooth. Spoon a little more peach filling on the centers, drizzle the glaze over the cookies, then enjoy!
Store leftover cookies in an airtight container for 2-3 days in the fridge or at room temperature. If storing in the fridge, let the cookies come to room temperature before serving.