A richly flavoured brunch for an indulgent weekend.
For the toasted brioche, bring a large saucepan of water to the boil, add the vinegar and a pinch of salt. Boil 4 of the eggs for 5 minutes. Remove the eggs from the saucepan using a slotted spoon, and leave to chill in a bowl of ice-cold water.
Crack the remaining egg into a bowl. Whisk with a pinch of salt and pepper.
Peel the boiled eggs. Prepare a shallow plate of flour and a separate plate of breadcrumbs. Dredge the boiled eggs in the flour, then dip into the beaten egg and roll in the breadcrumbs. Set aside on a tray in the fridge until needed.
Heat the oil in a deep-fat fryer to 180C. Alternatively, pour the oil into a deep, heavy-based pan to a depth of 2cm/¾in and heat until a breadcrumb goes brown when dropped in. (Caution: Hot oil can be dangerous. Do not leave unattended.)
Deep-fry the eggs until golden-brown. Remove with a slotted spoon, drain on kitchen paper and season with salt.
Heat a frying pan, add the butter and olive oil. Add the shallot and gently fry for 3 minutes, until just softened. Add the garlic and mushrooms and cook until the mushrooms have released their liquid and are tender. Finish with the dill and black truffle and season with salt and pepper.
For the mayonnaise, put the egg yolks, vinegar and mustard in a food processor and blend until pale and creamy.
With the motor running, pour in a steady stream of oil until the mayonnaise is thick (you may not need all the oil). Just before serving add the dill and truffle and blend.
When you are ready to serve, heat a clean frying pan and lay the brioche in the hot pan. Toast each side until golden-brown.
To serve, cut a hole in the slices of brioche and sit the eggs in the holes. Dress the plate with mushrooms and mayonnaise and shavings of fresh truffle.
