Directions:

1. Cut the red peppers into quarters, removing the stems, seeds, and membranes. Lay the peppers flat on a foil-lined rimmed baking sheet, skin-side up. Broil the peppers until the skins are completely charred and blackened, approximately 10 to 15 minutes. Transfer the charred peppers to a mixing bowl, and cover with plastic wrap. Let the peppers steam for 10 to 20 minutes, until they are cool enough to handle. Peel the charred skin off the peppers. Set the roasted red peppers aside.
2. Add the capers, olives, garlic, pepperoncini peppers, and the 1/2 cup of olive oil to a food processor, and pulse until the ingredients are roughly chopped. Transfer the pulsed ingredients to a large mixing bowl, and add the red wine vinegar, fennel seeds, dried oregano, celery seeds, chili flakes, and shallot. Fold all the ingredients together. Keep in mind that some excess oil is a good thing—it will soak into the bread and make the sandwich delicious. Taste the olive mixture. It should taste strongly acidic, salty, and spicy. Adjust the flavor with more salt or red wine vinegar as necessary. Set the mixture aside.
3. Peel the carrots and cut them into planks about 1/4-inch thick. Place the carrots on a foil-lined rimmed baking sheet, drizzle with olive oil, and toss the carrots so they are coated on all sides. Season with a pinch of salt. Broil the carrots until they begin to caramelize, approximately 6 to 8 minutes. Set the carrots aside.
4. Cut the cauliflower into florets, transfer to a mixing bowl, and toss with olive oil to coat. Arrange the cauliflower on a foil-lined rimmed baking sheet, season with salt, and broil until the florets begin to char and caramelize. Keep a close eye on the cauliflower to prevent it from burning. Remove the cauliflower from the oven when the tops of the florets begin to turn dark. When the cauliflower is cool enough to handle, gather 2 cups of the roasted florets and roughly chop them. Any extra roasted cauliflower can be saved for a different use. Transfer the chopped roasted cauliflower to a mixing bowl and season with a splash of red wine vinegar. Taste it. Adjust with salt as needed.
5. Time to assemble the sandwich. Slice the bread in half with a serrated knife. If the bread seems too tall, use the serrated knife to trim away some of the middle of the bread. Spread the olive mixture onto both halves of the bread, allowing some of the extra oil to soak into the bread. Starting with the bottom piece of bread, lay down the carrots, followed by the cauliflower. Tear the basil leaves with your hands and place them on top of the cauliflower. Next, add the provolone, followed by the roasted red peppers. Place a handful of arugula onto the top piece of bread. If there is excess oil leftover from your olive mixture, drizzle some of this over the arugula. Close the sandwich, slice it into wedges, and enjoy.