In a stockpot, heat oil over medium-high heat. When oil is hot but not smoking, add onion and garlic and stir until onions are soft and translucent, 5 to 7 minutes.

Add corn, bell pepper, salt, black pepper, and cayenne pepper (if using) and continue to cook, stirring occasionally, for another 3 to 5 minutes.

Add tomatoes and water or broth, and bring to a boil. Reduce heat and simmer until liquid starts looking cloudy and yellow, about 10 minutes.

Using an immersion blender (or in batches in a countertop blender or food processor) purée about half of the soup until smooth.

Whisk in half-and-half and basil.

Taste, and adjust seasonings if needed.