Heat oven to 400°F. Line cookie sheet with cooking parchment paper. Unroll dough on cookie sheet.
Spread Boursin cheese evenly over dough. Top with spinach, artichoke hearts, onions, lemon peel, mozzarella cheese and Parmesan cheese. Sprinkle with salt and pepper.
Roll up dough, using parchment paper to help roll; press seam to seal. Place bread seam side down on paper-lined cookie sheet. Brush with oil.
Bake 20 to 25 minutes or until light golden brown. Cut into slices. Serve warm.