Preheat oven to 300 degrees F. Line a cookie sheet with a silicone liner or mist the sheet lightly with cooking spray. Set aside.
In a large bowl, cream together the butter and sugar. Add in the egg YOLK and the vanilla and beat to combine. Lastly, add in the flour until a soft dough forms. This recipe makes very few cookies, by the way, but it's easily doubled.
Quickly whisk the egg white for a few seconds to break it up. Using a cookie dough scoop, roll Tablespoon-sized balls of dough into balls and quickly coat in the egg white, then dredge into the graham cracker crumbs to coat. Place about 2" apart on the prepared baking sheets.
Bake for 5 minutes, then remove from the oven and gently press an indentation in the middle using a teaspoon or wooden spoon handle, careful not to puncture completely through the cookie. Return to the oven and bake for an additional 10 minutes. Cool completely on the baking sheet.
Place the chocolate spread into a resealable plastic baggy and snip off the corner. Pipe into the indentations of each cookie; top with a pinch of marshmallow bits. Serve immediately.