In a large pot, combine the salt, water and potatoes and bring to a boil.
Cook until the potatoes are fork-tender, approximately 25-30 minutes.
Remove the pot from the heat and let sit for 5-7 minutes.
Cut potatoes in half lengthwise or slice.
Stir together olive oil, mustard and lemon juice in a bowl for the dressing.
Toss potatoes with remaining ingredients and then add dressing.
Serve immediately.