Thinly slice half the cucumbers and half the scallions crosswise. Set aside.
Coarsely chop remaining cucumbers and scallions; transfer to a large bowl. Add the dill, garlic, lemon juice, buttermilk, and yogurt; stir gently. Season with S&P and puree in a blender until liquefied. (Blender will give a smoother result than a food processor.)
Transfer soup to a large bowl and add the reserved sliced cucumbers and scallions. Adjust seasoning with S&P and Tabasco to taste. Chill at least 2 hours before serving.