Cut the kernels off of the cobs. Reserve the kernels and 3 of the cobs.

In a large sauté pan, heat the oil over medium-high heat. Stir in the onion, lower the heat to medium-low, and cook, stirring, until soft but not browned, 10 to 15 minutes.

Add the reserved kernels and cobs, 4 cups water, the bay leaf, and 1-1/4 teaspoons salt. Bring to a boil, then lower the heat and simmer for 30 minutes. Remove and discard the cobs and bay leaf.

Add the ice and stir until melted. Working in batches, blend the soup, adding water as needed, until completely smooth and creamy with great body but not too thick. To achieve the silkiest texture, use a powerful blender or pass the soup through a fine-mesh sieve after blending. Season to taste with salt. Cover and chill the soup for at least 3 hours.

To serve, ladle the soup into chilled bowls and garnish with spoonfuls of the red pepper puree.