Preheat the oven to 350°F. Line a baking sheet with parchment paper and set it aside.

In a mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until fully combined and smooth. Then add the egg and vanilla extract, mixing again until incorporated.

Add the all-purpose flour, 1 cup finely crushed graham crackers, salt, baking soda, and baking powder to the wet ingredients. Mix gently just until the flour mixture disappears and the dough comes together.

Using a 1/4-cup cookie scooper, portion out 8 equal cookie dough balls. Roll each ball between your palms to smooth, then roll them in the 1/3 cup of finely crushed graham crackers to coat.

Place the coated cookie dough balls on the prepared baking sheet. Gently flatten each to about 3/4 inch thickness. Bake in the preheated oven for 9-10 minutes. Once baked, let the cookies cool on the baking sheet for 10 minutes before transferring them to a wire cooling rack.

In a stand mixer fitted with a paddle attachment, whip the softened cream cheese and butter together until smooth and creamy.

Add the powdered sugar and vanilla extract to the cream cheese mixture. Mix on high speed for 2-3 minutes until the frosting is light and fluffy.

Fill a piping bag fitted with a large round tip with the cream cheese frosting. Pipe the frosting onto each cooled cookie evenly.

Drizzle raspberry jam over the frosted cookies for a tangy and sweet finish. Serve and enjoy!