Melt butter in a large pot and cook onion and carrot for 5 minutes. Add garlic for 30 seconds.
Add chicken and hot-dog slices and cook, stirring, for 3 minutes until the outside of the chicken turns pale. Pour in broth and bring to a gentle simmer.
Add macaroni and cook for 7 to 9 minutes, following the package time, until nearly tender.
Stir in cabbage, evaporated milk, salt and pepper. Simmer gently for 4 to 5 minutes until the cabbage is soft and the chicken reaches 165°F.
Let stand for 2 minutes, stir and serve while plenty of creamy broth remains around the noodles.