Rub the beef all over with olive oil and place in a shallow non-metallic dish with the garlic, cracked peppercorns and thyme. Rub all over the meat and cover with clingfilm. Marinate for at least an hour at room temperature, or, if possible, in the fridge overnight.
To make the lemon aioli, break the egg into the food processor and add the garlic, half a teaspoon of salt and the vinegar, sugar, lemon rind, mustard and half of the olive oil. Secure the lid and whizz for 10 seconds.
Leave to stand for a couple of seconds, then turn on again and pour the remaining olive oil and sunflower oil through the feeder tube in a thin steady stream. This should take 25-30 seconds. Switch off the machine, take off the lid, scrape down the sides, and whizz again for 2-3 seconds, then season to taste. Transfer to a bowl, then cover and chill until needed.
When ready to cook, if using a charcoal barbecue, light it 30 minutes before you want to start cooking. If using a gas barbecue, light it 10 minutes beforehand. Alternatively, use a griddle or frying pan. Brush the excess marinade off the beef and cook over hot coals for 5 minutes, turning frequently until the outside is well browned, then transfer to a platter and leave to rest for up to 30 minutes.
Slice the beef as thinly as possible and arrange on a serving platter. Add small piles of the beetroot, radish and watercress. Invite guests to create their own rolls by smearing a slice of beef with a little of the creamed horseradish, adding some beetroot, radish and watercress if desired, then rolling up the beef and dipping it into individual bowls of the lemon aioli.