Place cashews in a small bowl. Cover with water. Soak for at least 30 minutes, or overnight. (I brewed water in a tea kettle, poured the boiling water over the cashews, and let them soak for 15 minutes. If you have a high-speed blender, they won't need to soak long.)
Add oil to a large pot (I used my dutch oven) over medium high heat. Once hot, add onion and a pinch of salt and sautee for about three minutes. Add celery and carrots and sauté for another five minutes. Add garlic and broccoli and sautee for another five minutes.
Add 5 cups water, salt, and pepper. Stir and bring mixture to a boil. Once boiling, reduce heat to low and simmer, covered, for 15 minutes.
Drain cashews. Place cashews and 1 cup water in a blender (I used my nutribullet). Blend until very smooth and creamy. There should be no clumps. Set the cashew cream aside.
Puree soup using a large blender or immersion blender. You'll likely have to do this in batches.
Once soup is pureed, stir in cashew cream. Season to taste with additional salt and pepper, if desired.