In a soup pot add the oil and add the onion for about 6-8 minutes until it is very soft and the edges begin to brown.
To prepare broccoli, start by removing the tough stems by cutting off the florets and discarding the thick stem. Then, cut the florets into smaller, bite-sized pieces. Next, add the broccoli to a pot along with water or vegetable stock. Cover the pot and leave it over medium heat for about 15-20 minutes or until the broccoli becomes very soft.
When done, add a pinch of salt and pepper and blend until creamy.
Check for seasoning and adjust if needed.
Notes
The broccoli and veggie stock mixture will be hot when you transfer it to your blender. Transfer it carefully, and make sure your blender is heat-proof. If it isn't, just let the broccoli mixture cool before blending.
This soup only has two main ingredients - onion and broccoli. Make sure they are the freshest possible to ensure you end up with a new and tasty broccoli soup.
There's no need to dice the onion into small pieces before sautéing. They end up blended into the soup, so larger chunks are fine.
When sautéing the onions in olive oil, use low-to-medium heat. You want the onions to be translucent, not browned or burned.
Add a clove or two of minced garlic and sauté with the onion for added flavor. If you want a heartier soup, add some cubed potatoes there.