Preheat the oven to 350. Add butter, brown sugar, and white sugar to a stand mixer. Mix on medium speed for 2 minutes. Add eggs and vanilla and mix until eggs are just combined.
Add flour, crushed graham crackers, cornstarch, baking soda, and salt. Mix on low until just combined.
Using a large cookie scoop (1/4 cup), scoop the dough out onto a lined or lightly greased baking sheet. Bake for 9-11 minutes, until cookies are just set. If the cookies are rounded when you pull them out of the oven, use the bottom of a glass cup to slightly flatten the cookies while they're still warm.
While the cookies are cooling, make the frosting. Add cream cheese and butter to a bowl or stand mixer. Mix on medium for 2-3 minutes. Add powdered sugar and vanilla and mix for another 2-3 minutes. Transfer the frosting to a piping bag with a round, open tip.
To make the raspberry drizzle, add raspberries to a pan over medium heat. Stir while the raspberries begin to break down. In a small bowl combine the water and cornstarch.
When the raspberry mixture begins to bubble, add the cornstarch slurry and stir in immediately. Cook for another 1-2 minutes, then take off the heat. The mixture should be pretty thick, but it will thicken up even more as it cools. Transfer the mixture to a bowl and place in the fridge to cool.
Once the cookies and raspberry drizzle have cooled, assemble the cookies. Pipe the cream cheese frosting onto each cookie in a swirl design. Then, add the raspberry drizzle. I like to add the drizzle to another piping bag with a small rounded tip, but you can also just drizzle it on with a spoon.
Keep any leftover cookies in the fridge in a sealed container for 3-4 days. Enjoy!