Place the broccoli, onion, garlic, and vegetable broth in a saucepan. Bring the broth to a boil, cover, and reduce heat. Simmer until broccoli is tender, about 8 minutes.
Put half of the broccoli and broth into a blender with half of the potato and cashews. Blend at high powder until smooth. Pour into another saucepan, and repeat with the rest of the broccoli, potato, and cashews.
Heat the soup, covered, on low for 10 minutes or so. Check seasonings and add salt, freshly ground black pepper, and a pinch of red pepper to taste.
Curried Cream of Broccoli Soup Variation Add 1 teaspoon of good, mild curry powder to the broth in the first step. Substitute a cooked, peeled medium sweet potato for the Yukon gold potato, and add a larger pinch of cayenne pepper to finish.