Add the vinegar to the pesto. Set aside.
Boil the potatoes until soft but not squashy, then drain into a colander and shake off any excess water. Tip into a bowl and, while still hot, pour on the pesto dressing, reserving 1 tablespoon. Mix gently, crushing the spuds a little as you mix, then add the broad beans and gently toss. Carefully spoon onto a platter then garnish with the eggs, almonds and mint, then drizzle with the rest of the pesto and serve.