Place everything except the cream into the Thermomix bowl and cook for 8 min/80°C/speed 4. Pour into a bowl or jug that preferably will not retain heat. Cover with a cartouche and leave on the bench for 2 hours before transferring to the fridge for 24 hours.
Pour into the churner and follow manufacturers instructions, but add the cream to the churn. If you are not confident that your churner will do the job with combining the cream, stir it through first before churning.
Thermomix method (no churner). Once the custard has cooled to fridge cold, transfer to a large tray or pour into an ice cube tray. Freeze overnight. Place all frozen egg nog into the Thermomix bowl and chop 10 sec/speed 8. Insert the butterfly and whip 1 min/Butterfly/speed 4 or until you are happy with the consistency. It will still require further time in the freezer to be scoopable at this point. At least 2 hours or more. It will be a soft serve texture immediately after whipping.