Using a blender, puree 1 avocado, the buttermilk and scallion whites. Add the lime peel and three-quarters of the lime juice. With the machine on low speed, blend in the ice cubes, 1 at a time, until smooth. Season with salt; refrigerate.
Meanwhile, coarsely chop the remaining avocado and transfer to a medium bowl. Add the tomatoes, feta cheese, scallion greens and the remaining lime juice.
Divide the soup among 4 bowls. Top with the avocado salad and tortilla chips. Serve with the remaining tortilla chips on the side.