Using a large saucepan or skillet over a medium heat, you will add the vegetable oil, butter, or margarine to melt. Add the thinly sliced celery stalks, the chopped green onions and minced garlic cloves. Stir to combine and then saute for about 5 minutes or until the vegetables are tender.

Slowly stir in the chicken broth, the shredded cabbage, thinly sliced carrots, cooked shredded corned beef, salt and pepper. Stir well and then cover with a lid. Bring to a boil and cook for about 2 minutes and then reduce the heat to the lowest setting. Simmer, while occasionally stirring for about 20 minutes or until all the vegetables are tender.

Using a small mixing bowl you will add the cornstarch and the milk and stir to combine well. Gradually stir this mixture into the meat and vegetables you are cooking.

Increase heat to medium and bring to a boil while constantly stirring. Boil for about 1 minute and then remove from heat.