Heat olive oil in a large soup pot over medium heat; cook and stir onion, celery, and carrots in the hot oil until softened, 5 to 7 minutes. Stir potatoes, cauliflower, bay leaves, thyme, and oregano into vegetables; cook about 5 minutes more.
Pour vegetable broth and 6 cups corn kernels and into vegetable mixture and bring mixture to a boil. Reduce heat to low and simmer until vegetables are tender, 35 to 40 minutes. Remove and discard bay leaves.
Place remaining 2 cups corn kernels, cashews, and nutritional yeast into a blender and add several large spoonfuls of simmering broth to blender. Work in batches if necessary, filling blender no more than half full per batch. Cover lid with a dish towel and hold lid down; pulse a few times before leaving on to blend until smooth. Stir cashew mixture into soup pot; season with salt and black pepper.