Prepare the Broccoli: Rinse the broccoli. Then cut the crown away from the stems. Cut the crown into bite-sized florets. Cut branch stems into small, bite-size pieces. Discard the main stem. You should have around 4 cups of florets and small stem pieces.
Heat the oil in a large pot over medium heat. Add the onion, celery, carrots, and potato pieces. Sautee until the vegetables are tender, about 10 to 15 minutes. Add garlic and cook for about a minute longer.
Then add water, bouillon, wine, nutritional yeast flakes, cashews, and broccoli florets/pieces. Bring to a boil, then reduce to a simmer.
Simmer for 20 minutes until broccoli is tender. Remove from heat and let cool slightly. Use tongs to remove half of the broccoli florets from the pot.
Blend the soup: Remove the center cap from your blender lid. Fill the blender only halfway. Secure the lid on the blender and top with a kitchen towel. Blend on low speed for a few seconds, then slowly increase speed to create a creamy soup. Transfer to a bowl. then repeat with remaining ingredients from the pan. Add about 3/4 of the reserved broccoli florets to the pureed soup, leaving some to place as a topping.
Season with salt and pepper to taste. Serve with broccoli florets and croutons.