Add the water, sourdough starter, bread flour, salt, sugar, and vanilla to a large bowl. Mix until no dry flour remains. The dough will be sticky and shaggy, which is normal.
Cover and let rest for 1 hour, sprinkle in crushed graham crackers (if using), then do one round of stretch and folds. With a wet hand, grab one edge of the dough, stretch it up, and fold it over itself. Rotate the bowl and repeat four to six times.
Cover and bulk ferment at room temperature for 8 to 12 hours, until the dough has doubled and is full of bubbles.
Line a 9x13 inch pan with parchment paper. Melt the butter and stir in the vanilla in one shallow bowl. In a second bowl, whisk together the crushed graham crackers, sugar, and cornstarch.
Lightly oil your hands. Pinch off a small ball of dough around the size of a golf ball, dunk it fully in the vanilla butter, then roll it in the graham coating until covered. Place it in the pan. Repeat to make 24 balls in a 6 by 4 grid, all touching. Reserve any leftover coating for the top.
Cover and proof for 1 to 3 hours, until the balls are puffy and have grown together.
Press a square of chocolate or chocolate chunks into the center of each ball, pushing it all the way down to the bottom. The dough springs up as it bakes, so a shallow piece will get pushed back to the surface.
Bake at 425 degrees F for 22 minutes.
Scatter mini marshmallows over the top in small clusters, two or three per ball, then sprinkle with the reserved graham coating. Bake for 3 more minutes, for 25 minutes total, until the marshmallows are puffed and golden. The internal temperature should read at least 190 degrees F.
Let cool for 5 to 10 minutes, then pull apart and serve warm.