Whisk eggs in a medium bowl. Stir in milk, Parmesan cheese, oregano and pepper. Set aside.

Cook sausage in a large skillet over medium heat until browned, stirring occasionally. Drain off any fat. Remove sausage from skillet.

Grate zucchini and carrots, slice the onions. Melt butter in the skillet. Add vegetables; cook and stir over medium heat until tender.

Top with sausage. Grate the Swiss cheese and add to the skillet. Pour egg mixture over vegetable mixture. Stir gently to combine.

Cook, without stirring, over low heat 8-10 minutes or until center is almost set. Remove from heat. Let stand 5 minutes before cutting into wedges; serve hot with honeydew slices.