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Grate the ginger, and combine with the sugar and water in a heavy-bottomed saucepan over medium heat, stirring occasionally – about five minutes.
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As the ginger/sugar mixture is heating, add the egg yolks to a large bowl and whisk to combine.
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Add 2 cups of the half and half to the saucepan, lower to medium-low, and heat till simmering but do not boil – this will take about ten minutes (better to go slow and not risk boiling). Make sure to stir occasionally, including scraping the sides of the saucepan.
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Add the hot mixture from the saucepan to the large bowl with the yolks in a slow stream, whisking constantly.
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Transfer the mixture back into the saucepan over low, and heat until the mixture thickens over the back of a spoon (about 170 degrees) – this will only take a few minutes.
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While the mixture is reheating in the saucepan, rinse out the bowl (or….don’t) and add the remaining half and half and vanilla extract to the bowl, setting a sieve over it. When the custard is properly heated, pour it through the sieve into the bowl, pressing out all liquid from the ginger solids, stirring to combine.
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Chill the mixture in the fridge until completely cool (at least three hours), then churn in your ice cream maker according to its instructions.
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While the mixture is chilling in the fridge, you can finely chop the candied ginger (if using) – adding this to the ice cream maker when it’s about 75% of the way through churning.