In a pot, heat about a tablespoon of olive oil. Cook onions in the oil until tender and translucent, be sure to stir often. Add your cream soup and milk to the onions, whisk to get all the clumps out. While that warms on low, in another pot, cook your frozen broccoli with a little water. Just follow the directions on the bag.
While that cooks, grate your cheese, and mix your cornstarch and water. Place the cornstarch mixture into your soup pot and whisk. (the cornstarch helps it thicken while also causing the cheese to melt into a creamier texture). Once your soup looks like it is getting nice and hot, give it another stir, then add the cheese on top. Do not stir the cheese in just yet.
By now your broccoli should be finished. Go ahead and drain the broccoli. Spoon it all on top of your cheese and let it sit there for a minute, this way the steamy broccoli melts your cheese. Then go ahead and stir it all together until nice and smooth, salt and pepper to taste.
That's it, you are done! Easy, peasy, creamy soup. Enjoy!