In a medium saucepan over high heat, combine the corn cobs (halved if they fit in the pot better), 2 cups diced potatoes, and stock and bring to a boil. Reduce the heat to low and simmer for 20 minutes, or until the potatoes smash easily with a fork when pressed against the side of the pot. Remove the corncobs and place in the pot you'll use to saute the vegetables in Step 3, even if you've already started that step.

Puree potato-stock mixture until smooth (use an immersion blender or standard blender.) Reserve.

While the broth simmers, warm the butter and oil in a medium-large pot over medium heat. Add the onion and sauté for 5 to 7 minutes, until the onion is tender and translucent. Stir in the reserved corn kernels, garlic, carrot, celery, bell pepper, extra diced potato and salt. Reduce the heat to low, cover, and cook for 15 minutes, stirring occasionally, or until the vegetables are tender (especially potato.)

Add reserved stock to the vegetables. Raise the heat and bring to a boil. Reduce the heat to low and simmer for 2 more minutes.

Season with salt and pepper to taste, and serve with chopped basil if desired.