Using an immersion blender, puree part of the mixture until it is thick and stew like, leaving some chickpeas whole. (if you don't have an immersion blender, use a blender or food processor and puree half of the mixture.)
Toast the bread slices and rub with the garlic half on both sides. In a wide shallow bowl, place the bread slice and spoon the chickpea mixture over the bread. Drizzle with olive oil and sprinkle with smoked paprika.