To make the cookie dough: Whisk the flour, baking soda, and salt together in a medium bowl; set aside. In the bowl of a stand mixer fitted with the paddle attachment, or by hand, mix butter and sugars until thoroughly combined. Beat in the egg, yolk, and vanilla until combined. Add dry ingredients and beat at low-speed just until combined - the batter should look a little lumpy. Stir in chocolate chips.
To assemble and bake: Lay half of the graham crackers out on the baking sheets - two crackers per sheet. Top each cracker with 3-4 pieces of chocolate then top the chocolate with two marshmallow halves, laying them side-by-side. Lay the remaining graham crackers on top of the assemble s'mores. Sandwich the s'mores between two large spoonfuls of cookie dough and using the remaining dough to wrap around each of the s'mores; the result should resemble a small cookie brick.
Space the cookies at least 4 inches apart on the two baking sheets. Bake for 20-24 minutes or until the tops and edges are lightly browned and the edges just lift off the pan with a spatula. (While baking, the s'mores will press down under the weight of the cookie dough and will sink further while cooling. Don't worry if the cookies don't end up completely covering the s'mores - it only adds to the charm here.) Transfer the baking sheets to wire racks and cool the cookies on the sheets for at least 5 minutes. Transfer the cookies to the wire racks and cool for another 5-10 minutes before serving. Serve warm or at room temperature.
For the cookie dough (Thick and Chewy Chocolate Chip Cookies):