In a medium saucepan, combine the potatoes, broth and 2 teaspoons of salt. Add enough water to just cover the potatoes. Bring to a boil over medium heat. Reduce heat to low and simmer until tender, 8-10 minutes.
Drain, reserving 1/2 cup of the cooking liquid and transfer to a large bowl. Add gherkin brine, 1 tablespoon of vinegar and 1/2 teaspoon pepper.
In an empty skillet, combine the reserved cooking liquid with onion and caraway seeds and bring to a simmer over medium heat. Pour the mixture over the potatoes and stir well. Let sit, stirring every so often, until the liquid is absorbed and thickened, about 8-10 minutes.
Meanwhile, in a liquid measuring cup, whisk together the oil, mustard and remaining 1 tablespoon of vinegar, 3/4 teaspoon salt and 1/2 teaspoon of pepper until emulsified.
To the potatoes, add the dressing, celery, eggs, gherkins and dill, then fold until evenly coated. Taste and season with salt and pepper. Serve at room temperature.