Take a speed peeler and make some parmesan shavings (using about half of the parmesan). When doing the shavings, place them on a tray or plate so that they don't break up as they are very fragile and then place them in the fridge until they are needed.
Then grate the other half of the parmesan using the side of the grater that has the smallest holes.
Split the grated parmesan into 4 piles and place on a non-stick baking tray, spread out each pile as thinly as you can into a round shape.
Place the baking tray onto the bottom of the shelf of a hot grill until the galettes (parmesan crisps) are a nice orange colour.
Remove from the grill and using a palette knife, take the galettes off the baking tray, putting them onto a plate table so that they cool down quickly. Place to the side until needed.
Take a bunch of the asparagus tips and cut the woody part off and discard. Cut the asparagus into lengths of about 3 inches (the trimmings can be kept and used in making a soup). Peel the skin from half way down the tip.
Cook the asparagus in boiling salted water for a couple of minutes, then take out and refresh in iced salted water. As soon as they are cold take out of the water and put them in the fridge until needed.
To make the white truffle dressing, take the mayonnaise, add the white truffle oil and a little cream. (Add the white truffle oil very slowly as it is very powerful so it is best to add and taste as you go along). Check the seasoning and put into the fridge until needed.
