Bring potatoes and water to cover to a boil; cook 8 to 10 minutes or until tender. Drain and set aside.
Cut off corn kernels, reserving 4 cobs, and set aside. Place cream in a stockpot over medium-high heat. Add reserved corn cobs, and simmer 40 minutes or until reduced to 2 1/2 cups. Discard corn cobs, and pour liquid through a fine wire-mesh strainer into a bowl, discarding solids.
Sauté shallot in butter 2 minutes or until translucent. Add corn kernels, peas, and sugar; sauté 6 minutes. Add strained cream and reserved cooked potatoes. Stir in bacon and basil, and cook until thoroughly heated. Season with salt and pepper. Garnish, if desired.