In a heavy sauce pan warm half the cream and half and half, and then whisk in the the muscovado sugar, cinnamon, salt, and vanilla. Bring to a gentle boil, stirring frequently. Take off the heat. Add the the ginger and lemon zest.
Whisk the egg yolks together other half of the cream.Temper with 1/2 cup of the warm cream mix. Gradually pour yolk mix into the rest of cream mix in the pan and stir over low heat, but do not boil. Cover with parchment paper and cool; then refrigerate at least 2 hours, even overnight.
Proceed to follow your ice cream maker directions and process as ice cream. Freeze in a container for a few hours for best results. If you like your ice cream soft and a bit runny, then do go ahead and enjoy this right away.