Preheat oven to 400 degrees F.
Cover a sheet pan with parchment paper. On a lightly floured surface, roll out the sheet of puff pastry to a 14-inch square. Lay it on the parchment paper.
In a medium bowl, blend together the mozzarella, ricotta and Parmesan cheeses.
Brush the center square of the pastry with pesto, leaving a 3-inch border. Sprinkle with ¼ cup breadcrumbs. Sprinkle with artichoke hearts. Spoon on half the mozzarella mix in dollops. Spoon on the caponata and sprinkle with 1/4 cup breadcrumbs. Lay the roasted peppers on top and then spoon on the remaining cheese mixture. Sprinkle with the last ¼ cup breadcrumbs.
Pull up the sides and corners of the puff pastry to cover the filling. Pinch the seams together to seal them. Pat the torta into a nice square block. Brush the torta all over with egg and sprinkle with sesame seeds.
Bake 35-40 minutes, until very brown and beginning to ooze cheese. Let sit 10 minutes before slicing.