Prepare grill. Brush 3–4 corn cobs with 2 tablespoons olive oil, and grill corn until as “done” as you like (I prefer some dark grill marks but not an overall char). Set aside to cool.
Using a sharp knife, carefully cut kernels off remaining ears of corn. Add kernels to a food processor or blender with 1 cup of the water. Puree until very smooth, about 2 minutes.
In a medium pot over medium heat, cook celery and onion in remaining 1 tablespoon olive oil, stirring occasionally, until veggies are translucent and tender.
Add corn puree, remaining cup of water, and potatoes. Bring to a boil, reduce heat, and simmer until potatoes are tender, about 25 minutes.
Carefully cut kernels off roasted cobs of corn.
Add kernels to a food processor or blender and puree with ½ cup heavy cream until somewhat smooth, about 30 seconds.
Add roasted corn puree and remaining heavy cream to the pot, and simmer until heated through.
Season with salt and pepper to taste, serve hot!