I wish you lots of luck.
I gave my daughter a hazel tree with the inoculated truffle about 5 years ago now. They have kept the tree in a pot/planter, and anytime now there may be truffles!!!! The tree has grown well, so there should be truffles - I hope. Next time I visit I am going to rummage.
I have some truffle flavoured oil (shop bought), but I don't like the smell of it. It is unfortunate, and I think a waste of money.
Truffles are best freshly grated/shaved, as you say, on scrambled eggs, risotto, pasta. I think that the areas where wild truffles are found are a very closely guarded secret here in the UK. It must be lovely to live in Italy!