Steam the cauliﬂower ﬂorets, potatoes and carrots separately until just cooked, then allow to cool. Cut the potatoes and carrots lengthways into 6-mm-thick slices. Using aspic cutters, cut a heart shape from each potato slice and petal shapes from the carrot slices. Set the shapes aside, then roughly chop the remaining pieces of potato and carrot.
Meanwhile, to make the dressing, mix all the ingredients together in a bowl. Mix the chopped potatoes with 2 tablespoons of the dressing and set aside the remaining dressing and the potato mixture.
Thoroughly oil a 6-cup pudding basin. Arrange some of the tomato slices decoratively in the bottom of the pudding basin. Having done so, continue the pattern with a few cucumber slices, radiating outwards from the tomatoes and up the sides of the basin. Put half the cauliﬂower ﬂorets carefully into the basin and arrange the chopped carrot around the edge. Next, spread the diced beetroot in an even layer and cover with 2 tablespoons of the salad dressing.
Place the remaining cauliﬂower on top, spread evenly with the potato mixture and cover with the remaining cucumber slices. Press the vegetables down gently but with sufficient ﬁrmness to pack them well together, then leave them to stand for 10 minutes.
Put a very large and decorative plate or cake stand on top of the basin, then swiftly invert both basin and plate. Keeping a tight hold, shake gently to free the salad, then carefully remove the basin and tidy up any loose pieces of salad.
Arrange the lettuce around the salad and garnish with the potato and carrot shapes and the chopped parsley. Pass the remaining dressing separately in a serving bowl.