Put the potatoes in a large saucepan, add the vegetable stock and garlic, season lightly with salt and pepper. Cover and bring to the boil, simmer for 7 - 8 minutes or until nearly tender. 2. Add the asparagus tips and continue to cook, uncovered, until the asparagus is tender.
Lift the asparagus onto a plate and set aside. Continue to cook the potatoes over a high heat until the stock has reduced to a sticky glaze to coat the potatoes.
Tip into a large bowl and add the asparagus. Set aside. Lift the garlic out and keep separate.
Put the softened garlic from the cooked potatoes, herbs, lemon zest and juice, oil and sugar together into a food processor or blender. Blend to form a purée then season with salt and pepper. Just before serving pour the pistou over the potatoes and asparagus, toss lightly together and pile into a serving dish.