Peel the cucumbers if you prefer a softer texture, though I usually leave the skin on for extra crunch and color. Using a mandoline slicer, cut them into very thin, even rounds. The thinner the slices, the better they soak up the dressing, so don't rush this step. Place all the slices into your large salad bowl once you're done.
In a separate medium bowl, whisk together the sour cream, white vinegar, sugar, and dill until smooth and well combined. Add the salt and black pepper, adjusting the seasoning to your taste. I like to whisk it a little longer than you'd think necessary, just to make sure there are no lumps left in the sour cream.
Pour the dressing directly over the sliced cucumbers in the large bowl. Gently toss everything together using a spoon or your hands until every slice is evenly coated. Take your time here so the dressing reaches every layer of cucumber, not just the top.
Cover the bowl with plastic wrap or a lid and place it in the refrigerator. Let it chill for at least 4 hours, though overnight gives even better flavor. This resting time allows the cucumbers to soften slightly and absorb the tangy, creamy dressing fully.
Once chilled, give the salad a quick toss again since the dressing may settle. Use a slotted spoon to serve so you leave behind any extra liquid that's released from the cucumbers. Serve cold for the best texture and flavor.