Halve the cherry tomatoes and add to a bowl with the lemon zest and a drizzle of oil. Season with sea salt and black pepper.
For the pesto, finely crush the walnuts, finely chop the basil leaves, then add the oil, balsamic cream and the dried chili peppers. Stir until well combined. Spoon into a bowl and add the pecorino cheese.
Divide the tomatoes and burrata between plates, spoon the pesto over the burrata and drizzle with oil.