Preheat pan and oven. Position a rack in the center of your oven and preheat to 375°F (190°C). Line baking sheets with parchment paper and set aside.
Combine dry ingredients. In a large mixing bowl, whisk together the flour, baking soda, and salt. Set aside.
Cream butter and sugar. In a bowl with a hand mixer, or in your stand mixer with paddle attachment, cream the butter and sugars together on medium-high speed for about 2 to 3 minutes until light in color and fluffy. Scrape down the bowl as needed.
Add eggs and vanilla. Add in the eggs, one at a time, beating to combine. Beat in vanilla extract. Scrape down the bowl as needed.
Add dry ingredients. On low speed, add in the dry ingredients and mix just until combined.
Add chocolate chips. On low speed, add the chocolate chips stirring just until combined.
Dip graham crackers. Dip a graham cracker square into melted butter and place onto baking sheet. These cookies won't spread as much so you can place them closer together, about an inch apart. I was able to get 16 cookies onto one cookie sheet.
Scoop cookies. Using a small cookie scoop or a tablespoon, scoop about 1 ½ tablespoons of cookie dough and place onto graham crackers.
Bake cookies. Bake the cookies in the center of your 375°F preheated oven for about 9-11 minutes. Cookies will not look quite done yet. Remove from the oven. and allow to cool on the baking sheet for 5 minutes. Transfer to a wire cooling rack to continue cooling.
Broil marshmallows. Set oven to broiler setting. Place one large marshmallow, cut side down on top of each cookie. Place cookie sheet back into oven (I broiled in middle of my oven, so they didn't burn). and broil for 1-2 minutes just until marshmallows are lightly toasted. Keep an eye on them so they don't burn! Every broiler is different, but mine took 1 1/2 minutes.
Add chocolate squares. Remove cookie sheet from the oven, and immediately place a Hershey chocolate square on top of each marshmallow pressing down slightly. Allow to cool on the baking sheet for 5 minutes. Transfer to a wire cooling rack to continue cooling.