Heat the broth in a large soup pot over medium heat. Add the cauliflower florets and cook until soft, about 15 minutes. Puree the mixture with an immersion blender, leaving it a bit chunky.
Alternatively, use a slotted spoon to remove the florets and puree in a blender or food processor. Return the pureed cauliflower to the pot.
Combine the ground chicken, breadcrumbs, pecorino, 1 tablespoon sour cream, half of the scallions, the garlic, 1 teaspoon lemon zest, 1 teaspoon salt and 1/4 teaspoon pepper in a medium bowl. Mix to combine. Form the mixture into 25 small, flat oblong-shaped nuggets.
Heat the oil in a large nonstick skillet over medium-high heat. Add the nuggets and cook, shaking the pan, until browned all over, 3 to 4 minutes. Remove from the skillet.
Bring the cauliflower puree up to a boil. Add 1 teaspoon salt and the remaining 1 teaspoon lemon zest. Add the nuggets and cover. Lower the heat to medium-low and simmer until the nuggets are cooked through, about 10 minutes.
Ladle 1 cup of the hot soup into a medium bowl. Whisk the remaining 3 tablespoons sour cream into the soup, and then pour the mixture back into the pot. Stir in the buttermilk and the remaining scallions. Ladle the soup into bowls and sprinkle with paprika.
Caution: When blending hot liquids, first let cool for 5 minutes or so, then transfer to a blender, filling only halfway. Put the lid on, leaving one corner open; this will prevent the vacuum effect that creates heat explosions. Cover the lid with a kitchen towel to catch splatters and pulse until smooth.