Pre-heat oven to 350°F.
To make the Tomato Confit: Place grape tomatoes, red onion, olive oil, basil leaves, salt, and black pepper in a small oven-proof dish and cover with a lid. Bake for 30 minutes, remove lid, and allow to cool to room temperature. Add yellow pepper and stir until evenly combined. Set aside.
To make the Calabrian Chili Pepper Aioli: Place mayonnaise, Calabrian chili peppers and basil leaves in a bowl. Using a hand-held immersion blender, blend until well combined. Refrigerate until ready to plate.
To make the Pistachio-Crusted Fresh Mozzarella: Place Parmesan cheese, panko breadcrumbs, basil, salt, and black pepper in a food processor. Pulse so the basil can break down and give a slight green color to the breading, about 1 minute and 30 seconds. Scrape down the side of the bowl and add pistachios. Blend again for 1 minute. Remove breading and place in a mixing bowl.
Slice ¼ inch off the shorter end of the fresh Mozzarella ball and set slice aside. Slice the remaining ball in half to create at least one 4-ounce slice. Using your hand, carefully press down on the slice until it is ½-inch thick and the width of the bun.
In a bowl, mix eggs with cold water until combined. Dip the slice the into flour (as needed), then egg wash, then seasoned Pistachio Breadcrumbs (start off using only half the Pistachio Breadcrumbs so you do not contaminate the whole batch; you may have extra). Place back in egg wash and back into Pistachio Breadcrumbs to create a double breading. Using your hands again, carefully mold the crusted cheese with the crust into a circle the size of the bun. Be careful not to break the breading. Set aside.
Flash fry four basil leaves in 375°F oil until crispy, about 20 seconds. Use the best one for the garnish. It should be crispy and vibrant in color.
Melt butter in a medium sauté pan and toast the bun in the butter, cut side down. Remove from heat once golden brown.
While the bun is toasting, deep fry the Pistachio-Breaded Fresh Mozzarella in 350°F to 375°F oil until golden brown and cheese is melty – do not burn; it should be oozy melty and hold its shape. Remove from oil and pat dry gently. Place the slice of Mozzarella on top of the fried Pistachio-Breaded Fresh Mozzarella so it slightly melts from the heat, with a point of cheese towards the front. Using a blow torch, torch for extra melt if desired.
To plate: Evenly spread 1 tablespoon of Calabrian Chili Pepper Aioli on each toasted side of the bun. Set top bun aside, aioli side up. Evenly distribute arugula on bottom bun over aioli. Top the arugula with approximately 2 tablespoons of Tomato Confit. Evenly drizzle balsamic glaze over Tomato Confit. Place the Pistachio-Crusted Fresh Mozzarella with the slice of Mozzarella centered over the Confit with Balsamic. Place folded prosciutto on top of the cheeses. Place the crown bun with the aioli on top; do not smash. In the center on top of the crown bun, place the reserved thin slice of fresh Mozzarella and carefully torch. Place the best fried basil leaf garnish on top.
