Preheat broiler. Toss bell peppers and 2 tablespoons of oil on a rimmed baking sheet; season with salt and pepper. Broil, turning occasionally, until skins are blackened in spots and blisters all over, 10–12 minutes. Transfer peppers to a large bowl, cover with plastic wrap, and let sit 15 minutes. Reduce oven temperature to 400° F.
Peel and seed peppers; cut into 1” strips. Toss peppers in a clean large bowl with onion, garlic cloves, sun dried tomatoes, olives, vinegar, red pepper flakes, oregano, and 4 tablespoons of olive oil and set aside.
Toss bread and remaining 2 tablespoons of olive oil on a clean baking sheet; season with salt and pepper. Bake, tossing occasionally, until crisp on the outside but still chewy in the center, 8–10 minutes. Let croutons cool.
Toss antipasti mixture, and croutons in a large bowl. Arrange on a platter with cheese; top with remaining all the herbs.