First, make the truffle sauce. Blitz the mushrooms in a mini food processor until very finely broken down. In a medium frying pan, warm 1 tsp sunflower oil over a medium heat. Once hot, fry the mushrooms for 3-4 mins or until reduced and just cooked through. Remove from the heat and allow to cool before combining with the remaining sauce ingredients. Transfer to the fridge and leave to infuse for a few hours, ideally overnight.
To serve, put the truffle sauce into a large piping bag fitted with a small nozzle (or, if using a disposable piping bag, snip off a small hole for squeezing out). Pierce the base of each burrata, and use the piping bag to fill with the sauce until each burrata is extra plump, being careful not to overstuff. Dress with drizzles of oil, shavings of truffle, if using, and cracked black pepper and salt. Serve with crispbreads.
