Halve and pit the avocados. Scoop the flesh into the bowl of a food processor.
Add the chopped English cucumber to the food processor and process until the mixture is pureed.
Pour in the soy milk, and add the chopped scallions, lime juice, salt, and a few grinds of black pepper.
Process again until the soup is completely smooth and creamy.
Taste the soup and adjust the seasonings as needed, adding more salt or lime juice if desired.
Transfer the soup to an airtight container and refrigerate for at least 1 hour, or until thoroughly chilled.
To serve, ladle the chilled soup into small bowls and garnish with paper-thin slices of red radish.
Don't be shy with garnish variations. Try a swirl of olive oil, a sprinkle of chili flakes, fresh cilantro, or diced tomato.
