In a large mixing bowl, combine the flour, salt, baking soda, and baking powder, chocolate chips, mini marshmallows, and crushed graham crackers, and whisk together.
In a separate mixing bowl, cream the brown sugar and softened butter together with a spatula. Add the sourdough starter, egg, vanilla extract, and whisk to combine.
Add the wet ingredients to the dry ingredients and fold to combine, making sure not to over mix the batter.
Cover the dough and refrigerate for at least two hours or overnight. (Do not skip this step.)
Line a baking sheet with parchment paper. Scoop the chilled dough into 2-tablespoon portions and roll into balls. Place on the prepared baking sheet and repeat with the remaining dough.
Preheat the oven to 375°F (190°C) and bake for 12-14 minutes, then remove from the oven. If the cookies look puffy, gently press them down with a wide spatula. If any marshmallow has oozed out from the sides, use a spatula or knife to tuck it back in and reshape the edges while everything is still warm.
Transfer the cookies to a cooling rack until they are completely cooled, and enjoy!