Place all the ingredients for the glaze in a small saucepan. Bring to the boil, then reduce the heat and simmer until the mixture reduces and is of a glaze consistency. Keep hot.
Make the parsnip purée. Steam the parsnips and potatoes until tender. Drain, if necessary, and place in a food processor or blender with the yogurt, horseradish relish (if using) and pepper to taste. Process until blended. Keep warm or reheat prior to serving.
Brush the tuna with the oil. Cook on a preheated, very hot griddle or barbecue, or in a frying pan or under a grill, for 1–2 minutes. Turn and spoon the glaze over the tuna. Cook for a further 1–2 minutes – it is best if moist and still slightly pink in the centre.
To serve, top a mound of the parsnip purée with a tuna steak and spoon over the remaining glaze. Serve with steamed green vegetables, if liked.