Prep Your Ingredients - Preheat the oven to 350°F (175°C) and line a cookie sheet with parchment paper. Crush the graham crackers and measure out all the ingredients.
Mix the Dry Ingredients - Whisk together flour, baking soda, salt, cinnamon (if using), and crushed graham crackers in a medium bowl. Set aside.
Cream the Butter and Sugars - In a Kitchen Aid Stand Mixer, Bosch Mixer, or a large bowl, beat the butter, brown sugar, and granulated sugar with a mixer until light and fluffy (about 2 minutes). Add the Wet Ingredients - Mix in the sourdough discard, egg, and vanilla extract until smooth.
Combine Wet and Dry - Gradually add the dry ingredients to the wet mixture, stirring until combined.
Fold in Chocolate, Marshmallows and Graham Crackers - Using a rubber spatula, gently fold in the chocolate chips, mini marshmallows, and pieces of broken graham crackers, being careful not to overmix.
Chill Dough - Chill dough in the refrigerator for a least 30 minutes.
Scoop and Bake - Scoop cookie dough balls onto the lined baking sheets, leaving about 2 inches between each cookie. Bake for 10-12 minutes, or until the edges are crispy and the bottom of the cookie is golden brown.
Cool and Enjoy! - Let cookies cool on the pan for 5 minutes before transferring to a wire cooling rack. Enjoy warm for the ultimate gooey marshmallow experience.