Bring a saucepan of salted water to the boil.
For the fillet steak, heat a frying pan over a medium heat. Rub the oil into the steak and season to taste with salt and freshly ground black pepper. Add the steak and the butter to the frying pan and fry the steak for 2-3 minutes on each side, then remove it from the pan to rest.
For the caramelised onions, add the olive oil, butter and onion slices to the same frying pan and cook for 8-10 minutes, or until the onions have softened and are golden-brown. Set aside.
For the buttered vegetables, cook the potatoes, carrots and asparagus in the salted, boiling water for 5-6 minutes, or until they are tender, but are not cooked through. Drain the vegetables and empty the saucepan. Return the partially-cooked vegetables to the emptied saucepan, add the butter and water and continue to cook the vegetables over a medium heat for 4-5 minutes, or until tender.
For the red wine sauce, heat the red wine in a small saucepan over a medium heat until the volume has reduced by half, then and add the beef stock. Add the arrowroot and stir until the sauce has thickened. Add the butter and stir in until is has melted.
To serve, spoon the caramelised onions onto a serving plate and place the fillet steak on top. Spoon the buttered vegetables onto one side and drizzle the red wine sauce around the edge of the plate.