Start by preheating your oven to 350°F (175°C). This ensures that your cookies bake evenly.
Line a baking sheet with parchment paper to prevent the cookies from sticking.
In a large mixing bowl, combine the melted unsalted butter, granulated sugar, and light brown sugar. Use an electric mixer to blend until the mixture is smooth and creamy.
Add the egg yolk, whole egg, and vanilla extract to the mixture. Beat until fully incorporated.
In another bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, stirring until just combined.
Gently fold in the graham cracker crumbs until they’re evenly distributed throughout the dough.
Using a cookie scoop, drop rounded tablespoons of dough onto the prepared baking sheet, leaving space between each cookie. Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown.
Once baked, remove the cookies from the oven and allow them to cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.
While the cookies are cooling, prepare the frosting. In a mixing bowl, beat together the softened cream cheese and softened butter until smooth. Gradually add the powdered sugar, followed by the salt and vanilla extract. Mix until fluffy and well combined.
Once the cookies are completely cool, spread a generous amount of cream cheese frosting on top of each cookie. You can use a spatula or even a piping bag for a more decorative touch.