Preheat oven to 450 degrees F.

Put unhusked corn and unpeeled garlic on a baking sheet and roast until corn is fragrant and husks are lightly browned, about 25 minutes.

Let cool, then remove husks and silks. Cut kernels away from cobs.

Cut 4 cobs in half crosswise with a heavy knife or cleaver. Discard remaining 2 cobs.

Peel the garlic. Set corn kernels and garlic cloves aside.

In a saucepan, combine broth, potato, the halved corn cobs and 3 cups water. Cover partially, bring to a simmer over moderate heat and adjust heat to maintain a simmer. Cook until potato pieces are tender, about 20 minutes. Discard corn cobs.

In a food processor, combine corn kernels, garlic cloves, potatoes (lift them out of the broth with a slotted spoon) and cornmeal. Puree, adding potato broth gradually through the feed tube.

Transfer soup to a sieve set over a bowl and press mixture through sieve with a rubber spatula, leaving corn skins behind.

Transfer soup to a clean saucepan. Stir in cream and reheat. Season to taste with salt, pepper and a pinch of sugar, if desired.