In a Dutch oven, bring potatoes, 1 teaspoon salt, and water to cover to a boil over medium-high heat. Reduce heat to medium-low; simmer until tender, about 10 minutes. Drain. Let cool to room temperature.
In a small bowl, combine shallot, vinegar, tarragon, pepper, and remaining 1 teaspoon salt. Slowly whisk in oil. Pour over potatoes; toss. Cover and refrigerate for at least 1 hour, stirring occasionally. Sprinkle with additional pepper. Garnish with tarragon, if desired.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/potato-tarragon-salad-recipe/