Place beetroot in a large saucepan, cover with water and bring to a boil. Cook 1 hour 30 minutes, or until a fork is easily inserted. Drain, reserving 4 tablespoons cooking water. Refresh under cold running water; leave to cool.
Cook potatoes in boiling water 20 to 30 minutes, or until just cooked. Drain, refresh under cold running water; leave to cool. Peel beetroot and potatoes, halve and slice thinly. Place in separate bowls.
Plunge tomatoes into boiling water 1 minute. Transfer to bowl of iced water. Peel tomatoes, cut in halves, remove seeds and dice flesh. Combine tomatoes and spring onions with beetroot. Add garlic, parsley, coriander and reserved cooking water.
To make spicy vinaigrette, whisk vinegar, oil, salt, pepper and cayenne pepper until combined. Stir two thirds vinaigrette into beetroot mixture and remainder into potatoes. Cover and refrigerate 30 minutes.
Just before serving, add salt, pepper and more vinegar to taste. Spoon beetroot salad onto a platter and arrange potato salad around it. Garnish with olives.