In another pan combine the milk, 2 tablespoon sugar and the minced preserved ginger. Stir over medium heat until the milk comes to a scalding temperature, just short of a simmer, then remove the pan from heat. Add the fresh ginger syrup into the milk mixture and stir well to blend. Cover and steep for 20 minutes.

In a small bowl beat the egg yolks and 1/4 cup sugar until the mixture is pale yellow, thick and falls in ribbons from the beater.

Put the heavy cream in a medium size bowl and cover with a strainer.

When the steeping time is over, bring the milk mixture to scalding again, stirring. Slowly add 1/4 of the scalded milk to the egg mixture and then pour the egg mixture back into the remaining milk. Cook over moderate heat, whisking slowly, until the mixture reaches a custard consistency. Do not let the mixture boil. Pour the custard through the strainer into the bowl of cream. Stir the liquid in the strainer to coax it through the mesh. Discard the ginger solids. Allow the mixture to cool completely, stirring occasionally. Once cool, the mixture may be sealed airtight and refrigerated 1-2 days before freezing.

Just before freezing, add the lemon juice and stir well. Freeze in an ice-cream maker or freeze in a shallow tray for 2 hours. Beat with a food processor and freeze again. Repeat this procedure.

When freezing process is completed, pack the ice cream into a plastic container, pressing it down to eliminate any air bubbles. Press a piece of plastic wrap directly on the surface of the ice cream to prevent formation of the ice crystals. Freeze for two more hours, but allow to soften slightly in the fridge before serving.