Cook potatoes in boiling salted water over medium-high heat until tender (15-18 minutes). Drain well, cool (25-30 minutes), then peel, cut into 3cm pieces and transfer to a large bowl.
Meanwhile, cook eggs in a saucepan of boiling water over medium-high heat until medium-boiled (6-7 minutes). Drain, refresh, peel, coarsely dice and add to potato.
Meanwhile, for aïoli, heat oil in a saucepan over low heat, add garlic and cook until just tender (4-6 minutes). Cool garlic in oil, remove with a slotted spoon, set aside (reserve oil). Process garlic in a small food processor to a fine paste, add yolk and, with motor running, gradually add reserved oil until emulsified. Add lemon juice, season to taste. Makes about 300ml.
Add remaining ingredients to potato and stir gently to combine. Add aïoli to taste (remaining will keep refrigerated for 3 days), season to taste, serve at room temperature.
This recipe is from the October 2010 issue of Australian Gourmet Traveller.