Preheat the oven to 400F. Heat a small amount of oil in a large skillet over medium-high heat, then add the potatoes and cook until slightly soft (about 5 minutes).
Add the red peppers and onions to the skillet and sauté until the onion begins to brown (about 5 minutes).
Add the sausage to the skillet and cook until browned (about 5 minutes). Then stir in the spinach and mozzarella cheese.
Once the spinach begins to wilt, add the salt, cayenne pepper and pesto and mix well.
Transfer the filling to a strainer and press out the excess liquid.
Cut the dough into four equal portions and roll each out into a 5-inch circle.
Spoon about 1/2 cup of filling onto one half of each turnover, leaving a small border.
Fold the dough over the mixture and roll the bottom edges over the top to seal the turnover.
Place the turnovers onto a greased baking sheet. Combine the water and egg white and brush over each turnover, then sprinkle with parmesan cheese.
Bake at 400F until golden brown (about 18 minutes). Let cool before serving (about 5 minutes).