Place the potatoes sliced in a large saucepan and cover with cold water. Add the 2 teaspoons salt and bring to a boil. Lower the heat and gently boil for 10 minutes or until the center of the potato’s slices are just tender. Be careful not to overcook them. Once ready, drain them and run cold water over them to stop the cooking process. (At this point the potatoes can be refrigerated for 2 days)
In a heavy 12-inch skillet heat the oil. Add the shallots and toss over medium heat until the thin slices become translucent, 1 to 2 minutes. Do not brown.
Add the potatoes and 1 tablespoon vinegar and gently toss over high heat for 3 to 5 minutes. Add the basil, salt, black pepper, and more vinegar to taste. Serve immediately.