Prepare the bread dough: In a large stainless steel bowl, combine warm water, sugar, and instant yeast. Let sit until foamy. Add bread flour and kosher salt, mix until combined. Cover and rest for 30 minutes.
Stretch and fold the dough: With wet hands, stretch and fold the dough from the edges into the center, turning the bowl and repeating at all four corners. Flip dough seam side down, cover, and rest 30 minutes. Repeat this process four times total.
Shape and proof the loaf: Lightly flour work surface, deflate dough, stretch into a rough rectangle. Fold top corners down in thirds like an envelope, seal edges, and roll to desired length. Place on parchment-lined baking tray, cover, and let rise 45-60 minutes.
Bake the bread: Preheat oven to 475°F (246°C). Score the loaf with three cuts. Add ice cubes to the oven to create steam, place the loaf inside, and bake about 20 minutes until golden and crusty.
Make the tomato sauce: Heat olive oil in a pot over low heat. Add chopped garlic and toast 30 seconds without browning. Add canned tomatoes, chili flakes, salt, pepper, and water. Blend with immersion blender until smooth. Simmer on medium heat for about 30 minutes until reduced by half.
Prepare chicken cutlets: Slice chicken breasts halfway through and pound to 1/4 to 1/2 inch thickness. Set up dredging stations: flour, beaten eggs, and bread crumbs mixed with salt, oregano, and Parmesan. Coat chicken in flour, then egg, then breadcrumb mixture.
Fry chicken cutlets: Heat about 3/4 inch oil in a pan over medium heat. Test oil temperature with breadcrumbs. Fry cutlets 3-4 minutes per side until golden. Drain on wire rack and season immediately with salt.
Toast the bread and assemble sandwich: Slice bread loaf in half, drizzle olive oil on cut sides, and broil until lightly toasted. Place two cutlets on bottom half, add tomato sauce (not too much), layer sliced fresh mozzarella, broil until cheese melts. Top with grated Parmesan and basil leaves, then cover with top half of loaf.