For the Chateaubriand, preheat the oven to 200C/400F/Gas 6.
Season the chateaubriand with salt and freshly ground black pepper.
Heat a large ovenproof pan until hot, add the oil and the butter then add the beef and seal on each side until browned, basting the beef.
Smoother the beef with the Dijon Mustard
Transfer to the oven and roast for 15-20 minutes, (depending how you like your beef).
Remove from the oven, turn over and allow to rest for at least 15 minutes.
Meanwhile, place the cherry tomatoes onto a roasting tray and place in the oven for 8-10 minutes until just bursting.
To make the béarnaise sauce, place the vinegar, white wine, peppercorns and shallot into a small saucepan and bring to the boil.
Simmer until the liquid has reduced by half.
Strain the liquid into a medium bowl.
Add the egg yolks and whisk well, then add the lemon juice.
Place over a pan of simmering water and whisk together until thickened and light in color.
Gradually add in the clear melted butter, whisking constantly.
Season with salt and black pepper and add the chopped tarragon leaves.
Turn off the heat and leave the bowl over the pan until ready to use
To serve, carve the rested beef into thick slices and place onto the serving plate. Serve with lovely roast potatoes and your favorite greens and the cherry vine tomatoes.