Heat the 1 tablespoon extra-virgin olive oil in a large saucepan over medium heat. Toss in the 1 medium onion and cook until softened, about 5 minutes.
Add the 2 smallish potatoes and 1 head cauliflower and cook, stirring frequently, for 2 minutes.
Add the 4 cups chicken broth and 1 cup cold water and bring to a boil. Reduce the heat to low, cover, and gently simmer until the veggies are tender, 20 to 25 minutes. If using a handheld immersion blender, purée the soup until smooth. If using a countertop blender, let the soup cool for at least 10 minutes, pour it into the blender, and process until smooth, working in batches if necessary. Return the soup to the pot and gently rewarm over low heat.
Add the 5 1/2 ounces soft blue cheese to the soup and stir until it melts. Season the soup with salt and freshly ground white or black pepper to taste.
Ladle the cauliflower soup into bowls and top with the extra blue cheese. If desired, you can let the soup cool and then refrigerate it for up to several days or freeze it for up to a month. The soup actually improves with time spent in the fridge.