Begin by roasting the red peppers: Preheat the oven to 350 degrees. Place the peppers on a sheet pan and bake them for one hour. Peel the peppers and remove the seeds. Slice the peppers thinly and chill.
While the peppers bake, make the chicken: Put the chicken on the baking sheet and sprinkle the salt, pepper, paprika, and garlic and onion powders all over the chicken. Drizzle on the olive oil. Bake for forty minutes or until the chicken is no longer pink in the middle. When the chicken is done, remove the skin and bones, and chop the chicken in half inch pieces.
Meanwhile while the chicken cooks, hard boil the eggs. Place the eggs in a two quart saucepan and cover them with cold water. On high heat, bring the water to a boil. Then, turn down the heat, and simmer the eggs for 15 minutes. Drain the eggs and peel them under cold running water. Chop the eggs in half inch pieces, and chill.
Also, make the vinaigrette by shaking up all the ingredients in a small jar.
Put all the arugula in a large bowl, or on a large platter. Arrange the cooked chicken, prosciutto, cucumbers, eggs, mozzarella and tomatoes in rows on the arugula. Drizzle on as much dressing as you like.