Place flour in a food processor fitted with a dough blade, and through the feed tube with the food processor running, slowly pour the proofed yeast mixture, until the dough comes together and is a cohesive mass. Transfer the dough to a floured board, and knead for about 5 minutes. Place in a bowl, cover with a clean dish towel and allow dough to rise, so that it roughly doubles in volume. (This will take about 30 minutes to an hour). The dough has risen enough if you make an indentation with your finger and it does not spring back.) Punch the dough down and allow it to rise again. (Allowing the dough to rise a second time gives it a finer texture.) Note: It will not rise as much the second time.
While the dough is proofing, begin to prepare the topping. Melt the butter over medium heat in a pan with a lid. Add apples and stir gently to coat with the warm butter. Combine cinnamon and sugar and sprinkle over the apples. Stir in the lemon juice. Cover and cook over low to medium heat for about 40 minutes, or until the apples are cooked through and tender.
Preheat oven to 450 degrees F. Stretch the dough out into a 14-inch circle which is thicker around the perimeter. Transfer dough to a pizza stone sprinkled with cornmeal. Top evenly with the cooked apple slices. Since the caramel topping and hazelnut, chocolate sauce are thick and awkward to spread, distribute spoonfuls of them evenly over the surface of the apple slices and the heat from the oven will make them melt onto the surface. Sprinkle with mini-marshmallows and drizzle with chocolate syrup. Bake for 10 to 15 minutes, or until the dough is nicely browned.