Char halved leeks on a hot griddle until soft, then infuse in oil at 50°C for 5 hours before leaving overnight.
Blend egg yolks and mustard, then slowly emulsify with 500g of the leek oil and whisk in vinegar and lemon juice.
Griddle a whole seasoned leek until charred and soft, then cover with cling film on a tray to keep warm.
Brush baguette slices with olive oil and toast on the griddle to make croutons.
Poach two egg yolks in warm leek oil for six minutes over low heat.
Fry girolles in foaming butter, add vegetable stock, then stir in vinaigrette off the heat.
Peel charred leek, toss in vinaigrette, and plate with poached yolks, mushrooms, and leek mayonnaise.
Garnish the dish with toasted baguette slices and fresh herbs.