For the vinaigrette, combine all the ingredients in a bowl, season. Whisk to combine.
Place the potatoes in a large saucepan of salted cold water. Bring to the boil over high heat. Cook for 10-15 minutes or until just tender. Remove the potatoes to a board, using a slotted spoon. Cool for 15 minutes.
Add the Broccolini® to the saucepan of boiling water and cook for 1-2 minutes until bright green and just tender. Drain and refresh in a bowl of iced cold water. Drain and pat dry with paper towel. Cut into 3-4cm lengths.
Thickly slice the potatoes and place in a large bowl, add the Broccolini®, tomatoes, olives and basil. Pour over the dressing and toss gently to combine. Spoon onto a serving platter or board, season, then scatter with parmesan.