Preheat oven to 350 degrees. Spread whole almonds in a single layer on a rimmed baking sheet, and spread sliced almonds in a single layer on another rimmed baking sheet. Toast in oven until brown and fragrant, 7 to 10 minutes (sliced ones will brown more quickly). Let cool.
Place bread in a bowl, and cover with cold water. Let stand 10 minutes. Squeeze out liquid, and discard.
Puree half of each of the whole almonds, bread, peeled cucumbers, and garlic in a blender. Add half of each of the oil and lemon juice, and puree. Transfer to a large bowl. Repeat.
Stir in buttermilk, salt, and pepper. Add water; if a thinner consistency is desired, add more water. Pass through a medium sieve. Refrigerate at least 1 hour (or overnight). If desired, thin with water before serving. Serve cold. Drizzle with oil, and serve with diced cucumber, tomato, scallions, parsley, and sliced almonds on the side.