Heat broiler. In a bowl, combine the beef, scallions, tortilla chips, chopped cilantro, cumin, ½ teaspoon salt, and ¼ teaspoon pepper.
Shape the mixture into 1-inch balls (about 24) and place on a broilerproof baking sheet. Broil until beginning to brown, 5 to 6 minutes.
Meanwhile, in a blender, puree the salsa with 1 cup water. Transfer to a large saucepan, add 2 cups water, and bring to a boil.
Add the meatballs, reduce heat, and simmer until cooked through, 2 to 4 minutes.
Serve the soup with the avocado, cilantro sprigs, and tortilla chips (if desired).