Mix together the bread flour, water, sourdough starter, salt, and brown sugar with a bread whisk or your hands until a shaggy dough is formed. Cover with plastic wrap or a damp towel and allow to rest 30 minutes.
After the rest time, add the chocolate chunks as you perform a set of stretch and folds. Grab one edge of the dough, gently lift until you feel maximum tension, then fold it across the dough. Turn the bowl ¼ turn and repeat. Complete two more folds until you have made a complete turn around the bowl. Cover and allow to rest for 15 minutes. Complete two more sets of stretch and folds every 15 minutes. Once you have completed the final set of stretch and folds, cover the bowl and allow to rest for bulk fermentation. Note: Bulk fermentation can last any where from 5-12 hours depending on the temperature of your home. In colder months, your dough will take longer to ferment, in warmer months, it will ferment faster. When completed, your dough should increase in size by about 50-75%. The dough should appear dome-shaped and will slightly pull away from the edge of the bowl. You will notice the dough has multiple bubbles on the surface and appears light and fluffy. When bulk fermentation is complete, turn the dough out onto a lightly floured surface. Gently spread the dough to form a large square.
Sprinkle 3/4 of the crushed graham crackers and marshmallows over the dough. Fold the dough into thirds. Sprinkle the remaining graham crackers and marshmallows over the top of the dough. Roll the dough into a ball.
Turn the dough, seam side down, then gently pull and twist the dough towards you a 2-3 times to tighten the dough into a ball. NOTE: Be careful not to overdo this step. You don't want the surface of the dough to break and spill out the filling. Transfer the dough to a lightly floured banneton, seam side up. Cover and chill in the refrigerator while you preheat the oven.
Place a 5 quart or larger dutch oven in the oven. Preheat the oven to 450℉.
Once the oven is preheated, remove the dough from the fridge and turn onto a piece of parchment paper.
Score the dough with a lame or sharp knife. Feel free to do any decorative scoring, then make a large X-shaped score from edge to edge for your expansion score.
Use the parchment paper to lift the dough, then transfer the loaf and parchment paper to the preheated dutch oven. Cover and bake for 20 minutes.
After the 20 minutes are up, remove lid and bake for another 15 minutes.
Remove the dutch oven, top the loaf with the remaining marshmallows. Return to the oven and let it bake for another 5-7 minutes until the marshmallows appear golden and roasted. Remove from the oven and top with remaining graham crackers and chocolate.
Allow to cool for at least 10-15 minutes before slicing the bread.