Prepare your wooden burning brick oven according to manufacturer's directions or preheat a conventional oven to 400 degrees F.
Place the peppers on a cookie sheet and season with salt and pepper. Roast the peppers for 15 minutes, turning periodically with tongs, so they are really charred and blistered on all sides. Put the peppers into a bowl, cover with plastic wrap, and steam for about 10 minutes to loosen the skins. Pull out the cores and seeds from the peppers and peel off the blackened skins; coarsely chop the peppers into chunks and set aside.
Season the flour with the garlic powder, dried oregano, and a fair amount of salt and pepper. Whisk the egg and milk together in a shallow bowl. Dredge the chicken pieces in the flour and tap off the excess. Dip each piece in the egg wash to coat, then dredge again in the flour. Place a large oven-proof skillet over medium heat and pour in about 1/4-inch of oil. Pan-fry the chicken in batches, skin-side down, until crisp, about 5 minutes. Turn the chicken over and brown the other side about 3 minutes longer. Remove the chicken to a side plate; it will not be completely cooked.
Carefully pour out the oil from the skillet and add 1/4 cup of clean olive oil. Put the pan back on the stove over medium heat. Add the anchovies, red pepper flakes, garlic, onion, tomatoes, lemon slices, capers, 1/2 of the roasted red peppers, and 1/2 of the basil; season with salt and pepper. This part of the recipe is going to be your base. What we are looking for is a fragrant vegetable pulp, so simmer for about 20 minutes, stirring often, until everything breaks down.
Add the remaining roasted peppers and basil. Tuck the chicken into the stew and pour in the wine and chicken broth. Transfer the chicken cacciatore to the hot oven and cook for 20 to 30 minutes until the chicken is cooked.