Follow the steps in order for the best result.
Begin by cutting the carrots lengthwise into quarters.
In a large skillet, bring approximately 2 inches of water to a rolling boil.
Add the quartered carrots to the boiling water and cook for 3 minutes.
Introduce the trimmed asparagus spears to the skillet and continue cooking for an additional 2-3 minutes, until the vegetables are tender-crisp.
Drain the vegetables thoroughly, then rinse them with cold water to halt the cooking process. Pat them dry with paper towels.
Unwrap the breadstick dough and cut each piece in half. Roll each half into a rope approximately 7 inches long.
Wrap one rope of breadstick dough in a spiral fashion around each vegetable (carrot and asparagus combination).
Place the wrapped vegetable sticks onto a baking sheet that has been lightly coated with cooking spray. Tuck the ends of the dough underneath the vegetables to secure them.
Brush the dough of each stick with the lightly beaten egg white.
In a small bowl, combine the grated Parmesan cheese and dried oregano. Sprinkle this mixture evenly over the prepared sticks.
Bake in a preheated oven at 375 degrees Fahrenheit for 12-14 minutes, or until the breadstick dough is golden brown and cooked through. Serve immediately.