Place the cashews in a bowl and add enough water to cover. Let sit for as long as possible, for at least an hour or even overnight.
Place a large pot over medium heat and add the olive oil and onion. Sauté until soft and translucent, about 5 minutes. Add the potatoes, broth and water, turn the heat up to medium high, and bring to a low boil. Reduce the heat to medium low and allow to cook for about 10 minutes or until the potatoes are fork tender.
Add the broccoli and sea salt to the pot and allow to cook for about 8-10 minutes more, or until the broccoli is fork tender. Remove from the heat.
Drain the water from the cashews, and add the cashews and 1/2 cup cold water to a blender. Blend for about 1 minute, or until the cashew cream is smooth and has the consistency of heavy cream.
Using an immersion blender, blend the soup until it has reached your desired consistency and texture. I like to leave it just a bit chunky with pieces of broccoli and potato for texture. Alternatively, if you don't have an immersion blender, you can remove the soup to a blender or food processor to blend, working in batches. If you choose this method, please be careful handling as the soup will be very hot.
Add the cashew cream to the pot of soup and mix well. Adjust sea salt and add black pepper to your desired preference.