In a large pot, heat 1 tablespoon of oil. Add the onions and sauté until tender, about 3 to 4 minutes. Add the cabbage and potatoes; stir. Add the broth and bring to a boil. Reduce heat and simmer, uncovered, for 30 minutes.
While the soup is cooking, heat the remaining oil in a small skillet and sauté the corned beef until crisp; drain on paper towels.
Add the carrots and half and half to the soup; simmer for 10 more minutes. Stir in the corned beef and adjust seasoning to taste with salt and pepper.
Notes
If you are preparing this recipe as GLUTEN FREE, just make sure your corned beef and chicken broth are both known to be GF.