Slice potatoes 1/4 inch thick and place in a large saucepan. Add salted water to cover by about 1 inch. Bring to a boil over medium-high heat. Reduce heat to medium and simmer potatoes until tender, 6 to 8 minutes; do not overcook. Drain and transfer to a bowl.
Add red onion, and Kalamata olives to the warm potatoes; toss gently.
Whisk vinegar, parsley, olive oil, thyme, salt, pepper, and sugar together in a small bowl. Pour dressing over potato mixture, tossing gently. Serve warm or at room temperature.
You may substitute 1/4 teaspoon dried thyme for the fresh.
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