Preheat the oven to 400 degrees F.
Heat a cast iron skillet over medium heat. When the pan is hot, add the olive oil and heat. Add the peppers and cook until they start to caramelize, about 5 minutes. Season with salt and pepper. Add the tomatoes and cook for 2 minutes.
Break the eggs into a large bowl. Season with salt and pepper and whisk well. Add the eggs to the pepper mixture and stir constantly until curds start to form. Cook until the mixture has begun to set but is still fairly wet.
Remove from the heat and scatter the olives and Serrano ham over the top. Place in the oven and cook for 5 minutes, or just it is mostly set, but still a little bit moist. Remove from the oven and sprinkle with the basil. Drizzle with extra-virgin olive oil and let sit for 5 minutes. Slice and serve.