Place the potatoes in a large saucepan and cover by 1 inch with water. Season with salt. Add bay leaf and bring to a boil over medium-high heat. Reduce heat to medium and simmer until potatoes can be easily pierced with a knife, 12 to 15 minutes. Do not overcook.
Meanwhile, whisk olive oil, white wine vinegar, Dijon mustard, salt, and pepper in a small bowl together until emulsified.
Drain cooked potatoes in a colander and cool until just warm enough to handle. Cut the potatoes into 1/2-inch slices and transfer to a large bowl.
Drizzle vinaigrette over potatoes, gently tossing to coat. Add shallots and parsley and toss lightly to combine.
Set the potato salad aside for about 10 minutes, allowing the flavors to meld. Taste and adjust seasoning if needed. Serve warm or at room temperature.
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