Preheat oven to 350°F. Place potatoes in a small bowl and drizzle with oil. Sprinkle with 1 teaspoon of the salt; toss to coat. Spread potatoes in a single layer on a baking sheet and bake until fork-tender; about 40 minutes. Remove from oven and cool for 15 minutes.
Cut each potato in half crosswise. Carefully scoop out potato pulp into a medium bowl leaving shells in tact. Place shells cut side up on baking sheet and bake in preheated oven until dry; about 10 more minutes. Cool completely; about 30 minutes.
Stir together potato pulp, sour cream, capers, parsley, dill, mustard, zest and remaining ½ teaspoon of salt. Spoon mixture generously into each potato shell.