1. Preheat oven to 425°.
2. Unroll dough onto a baking sheet coated with cooking spray; pat into a 15 x 10–inch rectangle.
3. Heat oil in a large skillet over medium heat. Add onion and sausage; cook 9 minutes or until lightly browned. Stir in eggs; cook 1 1/2 minutes or until set. Remove from heat.
4. Sprinkle Monterey Jack lengthwise down center of dough, leaving about a 2 1/2-inch border on each side. Spoon egg mixture evenly over cheese. Sprinkle cheddar over egg mixture; top with jalapeño peppers.
5. Make 2-inch-long diagonal cuts about 1 inch apart on both sides of dough to within 1/2 inch of filling using a sharp knife or kitchen shears. Arrange strips over filling, alternating strips diagonally over filling. Press ends under to seal. Brush with egg white. Bake at 425° for 15 minutes or until golden brown. Let stand 5 minutes. Cut crosswise into slices.