Combine the basil, nuts, lime juice, salt, and oil in a food processor and pulse several times. Scrape down the sides once or twice and continue to pulse until you get a chunky, scoop-able pesto. Set aside until the soup is ready.
In a medium pot, combine the pears, corn, ginger, and water. Cover and bring to a boil, then reduce to a simmer and cook for 10 minutes. Turn off the heat and allow the soup to cool for 15 to 20 minutes. Once cooled slightly, purée the soup in a blender in batches until smooth. For a perfectly smooth soup, pass the liquid through a fine mesh strainer. Return the soup to the pot over low heat and stir in the salt and coconut milk. Once warmed through, the soup is ready to serve. Add a generous spoonful of the pesto to each bowl of soup.