Slice cucumbers in half and clean out seeds. Then grate and drain them through a fine mesh sieve overnight or squeeze out moisture with a kitchen towel.
Combine yogurt, garlic, oil, vinegar, and salt in a large bowl and put in cooler overnight. The next day, transfer grated cucumber, fresh dill, and white pepper to yogurt mixture and stir. Keep chilled.
Serve with raw vegetables and warm pita or add to any grilled meats or vegetables.