Add the potatoes to a large pot and fill it with cold water. Add 1/2 teaspoon of salt and bring to a boil. Let everything boil until the potatoes are fork-tender, around 10 minutes. Drain and set aside.
In a bowl, whisk together the finely chopped red onion, mustard, white vinegar, olive oil, sugar, salt, and pepper.
Peel the still-warm potatoes and slice them into cubes. Toss through the dressing, ensuring all the potatoes are well coated. Add the sliced cucumbers and serve immediately.