Place the lemon peels in a pitcher or jar and cover with the Everclear. Cover and let steep for at least 1 week or up to 1 month.
When ready to make the cream, add the half and half to a pot and heat on medium low. Add the sugar and vanilla and stir constantly until sugar is dissolved. Remove from the heat and let cool completely.
Strain the lemon peels from the alcohol and pour the infused alcohol into the cooled cream. Stir well to combine. Divide into bottles and store in the freezer until ready to drink.