Preheat oven to 400 degrees F. Line a baking sheet with parchment paper and coat with cooking spray.
Combine the olives, sun-dried tomatoes and oil in a food processor and pulse until the mixture forms a rough paste.
Lightly flour a work surface. Roll dough into a 14x10-inch rectangle. Spread with olive mixture, leaving a 1-inch border around the dough edges on all sides. Top mixture with overlapping slices of cheese. Add the spinach in an even layer on top. Add the red pepper strips in a single layer, long sides parallel to the long sides of the dough rectangle.
Fold 1 inch of dough over the filling on the short sides of the rectangle. Fold the long ends over the filling, pinching the dough together at the corners. Roll the dough, starting at one of the long ends, as tightly as possible. Pinch the seam to seal.
Transfer the roll, seam side down, to the prepared baking sheet and brush with the egg. Bake 25 minutes, or until the bread is golden brown.
Loosen the bottom of stromboli from the foil with a spatula. Transfer to a cutting board, slice into 1-inch pieces and serve.