Wash the cucumbers thoroughly. Using a sharp knife or mandoline, slice them into thin rounds about 1/8-inch thick.
Place the sliced cucumbers in a colander set over a bowl or in the sink. Sprinkle with 1 teaspoon of salt and toss gently to coat evenly.
Let the cucumbers sit for 15 minutes to draw out excess moisture. This step prevents your salad from becoming watery.
While the cucumbers rest, prepare the dressing. In a medium bowl, whisk together sour cream, white vinegar, sugar, and black pepper until smooth.
Rinse the salted cucumbers under cold water to remove excess salt, then pat them dry with a clean kitchen towel or paper towels.
Add the dried cucumbers to the dressing bowl along with the chopped fresh dill.
Gently fold everything together until the cucumbers are evenly coated with the creamy dressing.
Taste and adjust seasoning with additional salt if needed. The salting step usually provides enough saltiness.
Cover and refrigerate for at least 15 minutes before serving to allow flavors to meld. Serve chilled.