Using hand mixer of stand mixer fitted with the paddle attachment, beat butter, granulated sugar, and brown sugar until smooth and combined. Beat in egg and vanilla, scraping the sides/bottom of the bowl as needed.
In a separate bowl, combine flour, 1 cup graham cracker crumbs, salt, and baking soda.
Add dry ingredients to the wet ingredients, and beat until combined. Chill the dough in the refrigerator for one hour.
Preheat oven to 375°F. Line two baking sheets with parchment paper.
Place ½ cup graham cracker crumbs in a shallow bowl. Using a 1½ tablespoon cookie scoop, scoop the cookie dough and roll in the crumbs. Place the cookie dough balls a couple inches apart on the prepared baking sheets.
Bake for 8-11 minutes, until the edges are set and the very center is still slightly underdone (do not overbake). If necessary, rotate the baking sheets from front to back and top to bottom once during bake time (if your oven bakes unevenly). Place the baking pans on wire racks to cool completely before proceeding with remaining dough. Unbaked dough can be stored in the fridge in between batches.