Start by preparing the peppers because they will take the longest. Preheat the broiler. Pull out the cores of the red peppers; then halve them lengthwise and remove the ribs and seeds. Toss the peppers with a little olive oil, salt, and pepper. Place them on a cookie sheet, skin side up, and broil for 10 minutes, until really charred and blistered. Put the peppers into a bowl, cover with plastic wrap, and steam for about 10 minutes to loosen the skins. Peel the peppers and roughly chop into chunks; 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 and then dredge with the flour again. Place a Dutch oven over medium heat and pour in about 1/4-inch of oil. Pan-fry the chicken in batches, skin side down, until crisp, about 8 minutes. Turn the chicken over and brown the other side about 10 minutes longer. Remove the chicken to a side plate, pour out the oil, and clean out the pot.
Put the pot back on the stove and coat with 1/4 cup of oil. Add the garlic, onion, tomatoes, lemon slices, anchovies, capers, red pepper flakes, half the roasted red peppers, and half 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 the remaining basil. Tuck the chicken into the stewed peppers and pour in the wine. Turn the heat down to low, cover, and simmer for 20 minutes, until the chicken is cooked.