Blanch the basil in boiling water for approx. 20 secs., refresh in ice-cold water, drain, gently squeeze. Puree the basil and oil for approx. 3 mins. until very smooth. Allow the oil to drain through a sieve lined with a cheesecloth.
Tear the burrata into pieces, arrange on plates with the cucumber slices, season. Drizzle the herb oil over the top along with the lemon zest and juice.