These golden, flaky rolls make an impressive party appetizer. Freeze leftover rolls up to 6 months. To reheat, cover loosely with foil and bake at 375° for 15 minutes. Uncover and bake 10 minutes, turning after 5 minutes.
Combine first 7 ingredients in a large bowl. Add 3 tablespoons oil; stir well to combine. Stir in pepper, egg, and cheese until well blended.
Line a baking sheet with parchment paper; coat well with cooking spray.
Working with 2 phyllo sheets at a time (cover remaining dough to prevent drying), brush 2 sheets lightly with remaining olive oil (long edge of sheets should be closest to you). Top with 2 phyllo sheets; brush lightly with oil. Arrange 2 cups spinach mixture in an even mound along phyllo edge nearest you, leaving a 1-inch border on either side. Fold sides of phyllo partially over mound; roll dough and filling, burrito-style, to form an 11 x 3-inch roll. Place roll, seam side down, on prepared pan. Repeat procedure with remaining dough, oil, and filling to form 5 rolls. Make 3 small slits in the top of each roll to allow steam to escape.
Bake rolls at 375° for 50 minutes or until golden brown and crisp. Carefully transfer to a wire rack; cool 20 minutes. Cut each roll diagonally into 6 slices.