In a large pot, combine the potatoes, onion, corn kernels and cobs, carrots, celery, pepper, broccoli and cauliflower, garlic, thyme, white pepper, cumin, and 6 cups water. Bring to a boil over high heat. Reduce the heat to medium-low and simmer for 30 minutes, or until the vegetables are tender. Remove the corn cobs and let cool. Remove 1 cup of the soup and puree in a blender with a tight-fitting lid, covered with a towel. (If you like a thicker soup, puree 2 cups.) Return the pureed soup to the pot and add the dill. Scrape corn cobs with back of a knife to remove the creamy corn bits from the kernel, and add the bits to the pot. Season with salt and stir well.