Slice the potatoes in 1/2”/12mm thick rounds or semi-circles (depending on size of potatoes). There is no need to peel.
Bring a pot of water to a boil and cook potatoes until just tender but still holding their shape. Drain and allow to cool slightly. Cooking time varies, but will be about 15-20 minutes.
Thinly slice pickles, radishes, and celery.
Make the dressing:
Diced the onion and finely chop parsley.
Add 4 tbsp/60ml olive oil, vinegar, mustard, sugar, salt, pepper, and parsley to a mixing glass or small bowl. Whisk to combine.
Add 2 tbsp/30ml olive oil to a large frying pan on medium-high heat. Add the onion and cook, stirring occasionally until beginning to brown, 7-10 minutes.
Remove from heat and add in the dressing. Stir to combine.
In a large bowl, combine the potatoes, pickles, radishes, and celery. Pour over the warm dressing and toss to combine.
Serve immediately for a warm salad. Can also be served cold.