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 blistered 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 2” strips. Toss peppers in a clean large bowl with onion, garlic, 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 pepper mixture, salumi, and croutons in a large bowl. Arrange on a platter with cheese; top with remaining all the herbs.