Cut carrots lengthwise into quarters. In a large skillet, bring 2 in. of water to a boil. Add carrots; cook for 3 minutes. Add asparagus; cook 2-3 minutes longer. Drain and rinse with cold water; pat dry.
Cut each piece of breadstick dough in half. Roll each piece into a 7-in. rope. Wrap one rope in a spiral around each vegetable. Place on a baking sheet coated with cooking spray; tuck ends of dough under vegetables to secure.
Brush with egg white. Combine cheese and oregano; sprinkle over sticks. Bake at 375° for 12-14 minutes or until golden brown. Serve warm.