Wash the potatoes and add them to a pot (don't peel them). Cover with water, salt the water. Bring to a boil and cook for about 20-25 minutes or until the potatoes can be easily pierced with a fork. Make sure to not overcook them (or they will fall apart).
While the potatoes are cooking, cook the broth in a small pot until reduced in half so you should end up with 2/3 cup of broth. Set aside.
When the potatoes are cooked, drain them and leave to cool down slightly - they should be cold enough to handle but still very warm.
If the broth got cold, heat it again until very hot, take off the heat. Add the vinegar, mustard, and sugar. Whisk until combined. Add finely chopped red onion. Add the sauce to a large bowl.
Now you need to combine the sauce and the potatoes - both should be warm!
Peel one potato, cut it into slices and add to the sauce, stir with a wooden spoon. Repeat for the remaining potatoes, adding them to the sauce and stirring after every added potato. The salad will look soupy at first, but it will thicken.
Now leave the salad for 30 minutes to rest and stir it every 10 minutes with a wooden spoon. After this time the potatoes should absorb some of the sauce and the remaining sauce should thicken.
Add the vegetable oil, season the salad with salt and pepper, stir everything together.
Garnish with finely chopped chives and enjoy! It tastes good warm and cold.