Preheat oven to 180C or 160C fan. Heat an ovenproof frying pan on high. Season beef with salt and freshly ground pepper and brown well on all sides. Transfer to oven and cook for 20-25 minutes.
Meanwhile, cut celeriac and potato into cubes. Place in a saucepan and cover with water. Add lemon juice and bring to boil. Cook for 15-20 minutes, until tender. Drain, return to saucepan and place on low heat for 1 minute until any excess water has evaporated. Mash well with milk and butter, until smooth. Season to taste. Keep warm on low heat.
Remove beef from pan, cover loosely with foil and rest for 5 minutes. Add remaining butter to frying pan on high heat. Cook mushrooms for 3 minutes, until golden. Remove from pan. Deglaze pan juices with wine and simmer for 1 minute. Add stock and mustard, reduce heat to medium and simmer for 5 minutes, until reduced by half. Return mushrooms to pan with tarragon and simmer for 1 minute.
To serve, spoon celeriac mash onto each serving plate. Top with sliced beef and spoon over mushroom sauce.