Prick sausages with a fork. Place chicken sausages in a large skillet and add 1 inch of water. Add 1 tablespoon extra-virgin olive oil to the skillet, 1 turn of the pan. Bring water to a boil, then reduce heat a little. Allow all the liquid to cook away, then brown and crisp the casings, 5 to 6 minutes. Deglaze the pan with stock or wine and cook it off, 1 minute. Remove sausages to a platter.
While sausage cooks, slice the peppers and onions and prepare the garlic. Once the chicken sausage comes out of the pan, add 2 tablespoons extra-virgin olive oil, 2 turns of the pan. Add veggies and garlic, season with salt and pepper and cook 10 minutes.
Place the giardiniera, parsley, basil and lemon zest in the food processor and grind into a relish.
Slice sausages on an angle. Fill each roll with a little relish, then peppers and onions then the sliced sausages.