Dry the chicken pieces well with paper towels and season them liberally with pepper and salt.
Warm the olive oil in an oven-safe pan over medium heat and add the chicken pieces skin-side down. Cook the chicken for about 7 minutes until its skin is brown and crispy. Turn the chicken over and cook for another 5 minutes until golden brown on the other side. Set the chicken aside.
Add the potatoes, garlic, and onion to the pan and cook for about 7 minutes or until the onion is translucent and the potato wedges are starting to brown nicely on the cut sides. Remove the vegetables, and keep them aside.
Pour wine into the pan and cook until reduced to 1/2 its original volume. Scrap the chicken bits and other browned bits to deglaze the pan. Return the potatoes, onion, and garlic to the pan and add chicken stock, parsley, and Italian seasoning. Stir them to combine, and add the chicken pieces on top.
Cover your pan and transfer it to a preheated oven. Roast for about 45 minutes or until the chicken is cooked through and no longer pink in the center. You can use a thermometer to check if the chicken is fully cooked. It should read165 degrees F.
Remove the chicken and vegetables and leave the liquid. Put it on the fire and allow it to simmer. Add butter, salt, and pepper to taste and stir for the next 5 minutes. Add peas to your sauce and cook for 2 minutes.
Serve hot. Serve the chicken on top of potato wedges with the sauce with peas on top of the potato wedges and garnish with the sauce and peas.