Preheat the oven to 350°F. In a mixing bowl, combine white sugar, brown sugar, butter, egg, and vanilla extract. Mix until smooth. Then, fold in the crushed graham cracker crumbs.
Gradually add the flour and baking soda to the mixture, stirring until a thick dough forms. Once combined, set the dough aside.
Prepare a double boiler by filling a pot with water and bringing it to a boil. Place a metal bowl over the boiling water. Add the marshmallows to the bowl, stirring with a wooden spoon until they become sticky. Add the corn syrup and continue stirring until the mixture is smooth, about fifteen minutes.
Grease a 9x9-inch baking pan. Divide the previously prepared dough in half. Spread one half of the dough evenly at the bottom of the pan.
Layer 4-5 whole graham crackers over the dough. Place the chocolate bars on top of the graham crackers.
Pour the smooth marshmallow cream over the chocolate bars. Layer with the remaining whole graham crackers.
Take the remaining half of the dough, tear it into pieces, and scatter them over the exposed marshmallows. (Note: As the bars bake, the dough will spread to cover any gaps.)
Bake in the preheated oven for 15-20 minutes, or until the top turns a golden brown.
After baking, remove the pan from the oven. Allow the s'mores bars to set for at least an hour before cutting into them. If you're feeling adventurous, you can also dig in right away for an ooey-gooey mess. Enjoy!