Preheat oven to 200°C. Line an oven tray with baking paper. Toss kumara with a good drizzle of olive oil on prepared tray, season with salt and pepper, and roast for about 25 minutes or until golden and tender.
In a bowl, mix red wine vinegar and sugar together and add red onion. Leave to marinate for about 15 minutes. Drain, reserving vinegar for the dressing.
Place asparagus in a pot or heatproof dish or bowl, and pour over boiling water to cover. Leave to stand for 5–10 minutes until asparagus is lightly cooked through (but still crunchy). Drain and place in a bowl of iced water to quickly cool (this helps it retain its bright green colour) then drain again.
Mix all dressing ingredients together.
Toss roast kumara, asparagus, parsley, walnuts, and half the dressing, half the pickled red onion and half the parmesan together. Scatter over remaining pickled red onion and parmesan, and drizzle with remaining dressing.