1. Preheat your oven to 375 F (190 C). Line two large baking sheets with parchment paper or silicone baking mats.

2. In a large mixing bowl, using an electric mixer, cream together the softened butter, granulated sugar, and brown sugar until the mixture is light and fluffy. This usually takes about 2-3 minutes. The color should lighten, and the texture should become airy.

3. Beat in the vanilla extract, sourdough discard, and the egg until just combined. Make sure to scrape down the sides of the bowl to ensure everything is fully incorporated. The mixture might look a little separated at this stage, which is normal.

4. In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt. This ensures the leavening agent and salt are evenly distributed throughout the dough.

5. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix, as this can lead to tough cookies. Stop mixing as soon as no dry streaks of flour remain.

6. Gently fold in the chocolate chips, mini marshmallows, and graham cracker pieces using a spatula. Distribute them evenly throughout the dough.

7. Drop rounded tablespoons of cookie dough onto the prepared baking sheets, leaving about 2 inches between each cookie to allow for spreading. Bake for 10-12 minutes, or until the edges are golden brown and the centers are just set but still look soft. The marshmallows will be melted and slightly toasted.

8. Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. This helps them set up and prevents them from breaking.