I got this recipe from my cousin. I remember eating it at her house when I was a little kid, so I finally asked her for the recipe. I tweaked it a bit. Here it is as I made it:
4 shredded carrots
1 head of cauliflower, cut very small
1 bunch of brocolli, cut very small
1/2 onion, cut very small
2 cans chicken broth
5 cups water
Add all these ingredients and cook for a short time, about 10 minutes. While it's cooking, make a white sauce in another bowl:
1 1/2 cups melted butter
1 c flour
2 1/2 quarts milk
Whisk together, trying to get lumps out. If you don't, it's not the end of the world. They boil out. Add the white sauce to the veggie pot. Let cook for awhile. About 15 minutes before you want to serve the soup, add Velveeta cheese. I bought the large package and used about a third of it, if that. Season with salt and pepper and whatever else you'd like.
Now, this is my own little addition. I wanted the soup creamier so I added a couple of handfuls of potato flakes or potato pearls. I wanted to add potatoes originally, and probably will next time, but I didn't have any this time. The potato flakes add some thickness to the soup so you can use it in bread bowls! It's perfect for this weather!