Preheat oven to 350°.
Unroll dough; unfold layers (do not separate into strips). Place layers lengthwise, end to end, into an 11 x 7-inch baking dish coated with cooking spray. Pinch ends in the middle to seal; press dough up sides of dish. Set aside.
Heat vegetable oil in a large nonstick skillet over medium-high heat. Add onion, garlic, and jalapeño; sauté 3 minutes or until soft. Add corn and the next 5 ingredients (corn through broccoli); sauté for 5 minutes or until vegetables are soft and liquid evaporates. Remove from heat, and cool 5 minutes.
Combine milk, egg whites, egg, and salt; stir well with a whisk. Sprinkle cheese over dough. Spoon broccoli mixture evenly into pan. Pour milk mixture over broccoli mixture. Place dish on a baking sheet. Bake at 350° for 45 minutes; cover and bake for an additional 10 minutes or until set. Let stand 10 minutes.