Cook the celeriac in a saucepan of lightly salted boiling water for 2 minutes until softened. Add the potatoes and cook for a further 2 minutes until just tender. Drain the vegetables and refresh under cold running water. Drain well.
Meanwhile, mix together the mayonnaise, yogurt, mustard, gherkins, capers and tarragon in a large bowl, season well and set aside. Add the celeriac and potato and stir well to combine. Cover and chill until required.
When ready to serve, heat the oil in a frying pan or griddle pan. Add the asparagus and fry for 2–3 minutes until just beginning to colour.
Divide the celeriac and potato remoulade between 4 serving plates. Top with the asparagus spears and serve immediately, drizzled with a little extra olive oil.