Place the potatoes in a medium saucepan. Cover them with cold water and add 1 tablespoon salt. Bring to a boil, then reduce to a simmer and cook until the potatoes are tender but still hold their shape, about 12 minutes.
Meanwhile, combine the lemon juice, mustard, shallot, honey and 1/2 teaspoon salt in a blender. Blend until smooth. With the blender running, slowly drizzle in the oil.
When the potatoes are cooked, drain in a colander and tap out any excess water so the potatoes are as dry as possible. Transfer the warm potatoes to a large bowl. Add the diced celery, vinaigrette, 1/4 teaspoon salt and 1/4 teaspoon pepper and toss to combine. Garnish with the celery leaves and lemon zest. Serve warm or at room temperature.