In a medium saucepan, combine potatoes, 2 teaspoons salt, and water to cover by 1 inch. Bring to a boil over medium-high heat. Reduce heat to medium; cook until fork-tender, about 15 minutes. Drain potatoes. Place in an ice water bath to stop the cooking process; drain well.

In a large bowl, stir together butter, mayonnaise, dill, mustard, vinegar, pepper, and remaining ¼ teaspoon salt until smooth. Stir in potatoes and peas until coated. Cover and refrigerate for at least 30 minutes. Garnish with dill and pepper, if desired.