Hearty Egg Drop Soup

When I was a kid, my mum made egg drop soup when we were sick, which makes sense. It's a very mild soup with, at it's essence, nothing but vegetable broth and eggs in it. I was feeling in the mood for some last night--I haven't had it in years--but I knew that the only way it would fly with Mike was if there was a lot more than broth and eggs. So I scrounged the fridge and came up with carrots, cabbage, and green onions, which was lucky 'cause I don't typically have green onions on hand. So, here's a heartier version of the typical soup.

Serves 4

2 T. oil
4 small carrots, diced
1/4 head of cabbage, shredded
7 c. vegetable broth (or chicken--I didn't have any broth or base, so I had to make my own a little earlier in the day and I only had veggies)
3 or 4 eggs--I like a lot in mine so I used 4, but you could just use 2 or 3 I guess.
4 green onions, diced

Directions:
1. Put oil in the bottom of a medium to large sauce pan, warm over medium heat. Add diced carrots and cook covered until carrots are tender. Add cabbage and cook, stirring frequently until cabbage is tender.
2. Add broth and turn up high. While the broth is warming, beat eggs until well mixed. When broth is at a rolling boil, slowly pour the egg in a thin stream into the broth. (You could also use a fork to stream it in, but I get impatient with that.) Be careful not to let the soup boil over while you're adding the egg. It will start foaming, so stop pouring, give it a gentle stir, and continue. You can also turn the heat down if you need to, but it need to keep boiling to cook the egg.
3. Serve warm and garnish with green onions.