Remove the beef from the fridge and let it come to room temperature. Score the fat using a sharp knife and rub it all over with the oil and salt.
Preheat the oven to 220C/425F/Gas 7. To make the crust, melt the butter in a pan and fry the onions until tender. Put the breadcrumbs in a large bowl. Mix together the mustard and water in a small bowl. Tip the onions into the breadcrumbs, add the mustard mixture and the eggs, season with salt and freshly ground black pepper and mix everything together to make a paste.
Spread the paste evenly over the beef, leaving the ends uncovered. Cover the paste with a piece of well-greased tin foil. Place the carrots in a large roasting tray and sit the beef on top of them. Add some water to the tin to avoid it from burning. Place the beef in the oven and immediately reduce the oven temperature to 200C/400F/Gas 6.
Cook the beef for two hours. Remove the foil and cook the beef for one more hour. Remove the beef from the oven and leave it to rest for at least 20 minutes while you make the gravy and Yorkshire puddings.
For the Yorkshire puddings, beat the eggs with the milk and salt. Sieve the flour twice to aerate it then beat it into the egg mixture to make a batter. For extra smoothness, strain the batter through a fine sieve. Place a Yorkshire pudding tin in the oven until hot then add a good amount of dripping to each mould. Return the tin to the oven and heat until the fat is smoking. The fat will now be very hot now, so take great care as you take the tin out of the oven. Ladle some of the batter into each mould until nearly full then return the tin to the oven, reduce the heat to 200C/400F/Gas 6 and cook for 15 minutes.
Carve the rested beef and serve with the Yorkshire puddings, carrots and home-made gravy.