Preheat oven to 200°C. Cut chicken breasts lengthwise into two halves without cutting completely through leaving one side attached.
Open the chicken breast and season both sides with salt and pepper. Place the crumbled feta cheese and chopped peppers on half of the inside of the chicken breast and fold the other half over to close.
One by one, dust the chicken breasts with flour, dip them into the egg and then coat with bread crumbs.
Heat olive oil and butter in a skillet. Add the chicken breast and cook for 5-6 minutes on each side until browned. Transfer the chicken to a baking sheet and bake for 15-20 minutes until cooked through.
For the tomato pesto
Blend all ingredients except walnuts until they are puréed. Pour the purée into a bowl and mix in the chopped walnuts.
For the lemon sauce
Heat the butter in a sauce pan until golden. Stir in the rosemary and then the lemon juice. Mix well. Serve the chicken breast topped with the lemon sauce and with a side of tomato pesto.