Bring the milk to just boiling point and then turn off the heat. Add the tea leaves to the milk and allow to infuse for about 3-4 minutes. Strain and set aside to cool completely in the fridge.
Beat the eggs and sugar until fluffy, about 2 minutes. Add the honey and continue to beat for another minute.
Measure out one cup of cooled milky tea (if you have less than a cup, top up with extra milk, if you have too much, discard) and add this, with the cream to the egg base and briefly mix.
Run the mixture through an ice cream maker until ready according to the manufacturer’s instruction (churn the ice cream).
Notes
Store the ice cream in a sealed container in the freezer.