Prepare the Blueberry Topping: In a medium saucepan, combine blueberries, lemon juice, sugar, and half of the water. Cook over medium heat for about 4–5 minutes until berries soften. Mix cornstarch with remaining water, then add to pan. Stir until thickened, about 1–2 minutes. Remove from heat and cool.

Preheat the Oven: Preheat to 350°F (175°C) and line a large baking sheet with parchment paper.

Cream the Butters and Sugars: In a mixing bowl, cream together butter, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes.

Add Egg and Vanilla: Beat in egg and vanilla extract until well combined.

Combine Dry Ingredients: Gradually add flour, crushed graham crackers, salt, baking soda, and baking powder. Mix until just combined.

Shape the Cookies: Portion dough onto prepared baking sheet, spacing 2 inches apart. Flatten slightly.

Bake: Bake for 9 minutes, watching for a light golden edge. Allow to cool on the sheet for 10 minutes.

Prepare the Cream Cheese Frosting: Beat cream cheese and butter until smooth. Gradually add powdered sugar and whip until fluffy.

Assemble the Cookies: Once cooled, frost with cream cheese frosting and top with blueberry mixture.