Place the chicken breasts on a baking sheet. Loosen the skin from the meat with your fingers, leaving one side attached. Place 4 basil leaves under the skin of each chicken breast. Pull the skin over as much of the meat as possible so the chicken won't dry out. With your hands, rub each piece with olive oil and sprinkle very generously with salt and pepper. Bake the chicken for 35 to 40 minutes, until the skin is lightly browned and the chicken is just cooked through. Set aside until cool enough to handle, then remove the meat from the bones. Cut the chicken in large dice pieces and set aside.
Melt 4 tablespoons of the butter in a large saute pan. Add the potatoes and onions, 1 teaspoon salt and 1/2 teaspoon pepper and saute over medium heat for about 10 minutes, until evenly browned and cooked through.
In a separate saute pan, melt the remaining 2 tablespoons of butter. Add the red peppers, garlic, thyme, paprika, tomato paste, 1 teaspoon salt and 1/2 teaspoon pepper and saute over medium heat for about 5 minutes, until the edges of the peppers are seared.
Add the chicken and the pepper mixture to the potatoes and heat through. Add the scallions and parsley, toss together and place on a serving platter.