Photograph: Tara Fisher
Bring the potatoes to the boil in a large pan of salted water. Simmer for 15-20 minutes, or until tender.
Meanwhile, make the dressing. In a bowl, whisk together the olive oil, lemon juice, garlic paste and mayonnaise. Season to taste. Heat the vegetable oil in a small pan, tilting so the oil collects in one area. Add the seeds and, when they start to pop, remove from the heat. Leave for 10 seconds then pour it all into the garlic dressing. Whisk well.
Drain the cooked potatoes and, if you like, when cool enough to handle, peel them. Halve or quarter, depending on their size. Tip into the dressing, along with the spring onions and radishes, and mix well. The potatoes will absorb the dressing as they cool. Season to taste.
Get ahead: make the salad a few hours ahead; chill but serve at room temperature.
Kitchen secret: add a little heat with some chopped green chillies, if you like.