Wash the cucumbers thoroughly. If desired, peel them, leaving some strips of skin for color and texture.
Slice the cucumbers thinly (about 1/8 inch thick) using a sharp knife or mandoline.
Place the sliced cucumbers in a colander set over a bowl. Sprinkle with 1/2 teaspoon of salt and let sit for 30 minutes to draw out excess moisture.
Meanwhile, soak the sliced red onion in ice water for 10 minutes to mellow its flavor. Drain and pat dry.
In a large bowl, whisk together the sour cream, vinegar, chopped dill, sugar, remaining salt, and black pepper.
After 30 minutes, gently pat the cucumber slices dry with paper towels.
Add the cucumbers and red onion to the bowl with the dressing. Toss gently to coat evenly.
Cover the bowl with plastic wrap and refrigerate for at least 1 hour before serving.
Before serving, give the salad a gentle stir. Taste and adjust seasoning if needed.
Transfer to a serving bowl and garnish with additional fresh dill.