Preheat the oven to 400 degrees F (200 degrees C). Dry chicken pieces well and season liberally with salt and pepper.

Warm olive oil in an oven-safe skillet over medium heat and add chicken, skin-side down. Cook until chicken is browned and skin is crisp, 5 to 7 minutes. Turn over and cook until golden brown on the other side, an additional 4 to 5 minutes. Remove chicken and set aside.

Add potatoes, onion, and garlic to the skillet and cook until onion is translucent and potato wedges are starting to brown nicely on cut sides, 5 to 7 minutes. Remove vegetables from skillet and set aside.

Pour wine into skillet and cook until reduced to 1/2 volume. Deglaze the pan by scraping chicken bits and other browned bits up. Return potatoes, onion, and garlic to the skillet. Add chicken stock, parsley, and Italian seasoning. Stir to combine. Add chicken pieces on top.

Cover and transfer to the preheated oven. Roast until chicken is cooked through and no longer pink at the bone, about 45 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).

Return the skillet to stove and remove chicken and vegetables, leaving liquid. Bring to a simmer. Add butter and stir until smooth, about 5 minutes. Salt and pepper to taste. Add peas to sauce and cook 1 to 2 minutes longer. Serve chicken atop potato wedges and garnish with pan sauce and peas.