Husk the corn and discard the silk. Rinse corn. In a 5- to 6-quart pan over high heat, brown 2 ears, turning as needed to toast all sides, until kernels are speckled dark brown, about 10 minutes. Let corn cool. Rinse out pan.
With a sharp knife or corn cutter, cut the toasted corn from the cobs; set aside 1/2 cup of the kernels. Also cut corn from remaining cobs.
Return pan to high heat; add butter, celery, onion, thyme, and garlic. Stir often until vegetables are slightly browned, 3 to 5 minutes.
Add all of the corn except for the reserved 1/2 cup toasted kernels. Also add potato, broth, and cream. Stir to mix, then bring to a boil, cover, and reduce heat. Simmer gently, stirring occasionally, until potatoes are easy to mash, about 20 minutes.
In a blender, whirl the cooked mixture, a portion at a time, until smoothly puréed. Rub the purée through a fine strainer back into the pan. Add salt and pepper to taste. Bring to a boil over high heat, stirring often.
Ladle the soup into bowls and top equally with the reserved browned corn kernels.