In a large bowl, combine the chopped cauliflower, diced red pepper, thin sliced shallots, jalapeno, carrot, white vinegar, salt, diced olives, chopped parsley, and grated garlic. Stir well to mix, then let it marinate for at least 30 minutes to enhance the flavors.

Take the large chicken breast and place it between two sheets of plastic wrap. Use a meat mallet to pound the chicken to an even thickness. Season with salt and pepper, then set aside.

Line up three dishes: one with flour, another with the beaten eggs, and the last with breadcrumbs mixed with grated parmesan cheese.

Dredge the seasoned chicken in flour, shaking off the excess. Then, dip it into the beaten eggs, ensuring it's fully coated. Finally, coat it with the breadcrumb mixture, pressing gently to adhere the crumbs well.

Heat olive oil in a skillet over medium heat. Once hot, carefully place the breaded chicken in the skillet. Fry until golden brown and cooked through, about 5-7 minutes per side.

In a separate pan, melt butter over medium-low heat. Add the Italian bread slices and toast them on both sides until they are golden and crispy.

Place the fried chicken on the toasted bread, generously ladle some tomato sauce over it, and sprinkle with grated parmesan and slices of provolone and mozzarella cheese.

Arrange the assembled sandwiches on a baking sheet and place them under the broiler. Broil for 2-4 minutes until the cheese is melted and bubbly.

Slice the sandwiches in half, serve hot, and enjoy with the prepared spicy giardiniera on the side.