1. Preheat the oven to 350°F.

2. Cook the macaroni according to the package instructions until al dente.

3. In a large skillet, brown the ground beef over medium heat. Drain to remove excess fat.

4. Add the minced garlic cloves and cook for an additional 1-2 minutes.

5. Add the pasta sauce and diced baby carrots. Simmer until the carrots are tender.

6. Add the green beans and continue to simmer until cooked through.

7. In a separate bowl, whisk together the eggs, milk, mayonnaise, and brown sugar. Then add the shredded cheddar cheese and mix well.

8. Add the cooked macaroni to the ground beef mixture and stir well to combine.

9. Pour the cheese mixture over the noodle-beef mixture and spread evenly.

10. Bake in the preheated oven for 20-25 minutes, or until the cheese is golden brown and the mixture is hot and bubbly.

11. Allow to cool slightly before serving and enjoy!