Combine the blueberries, 1/2 cup sugar, water, and ginger in a medium saucepan over medium-high heat. Bring mixture to a boil; reduce heat to medium and simmer, stirring occasionally, 10 minutes. Remove from the heat and cool 20 minutes. Remove ginger slices and discard. Transfer blueberry mixture to a blender and puree. Pour into a large bowl; reserve.

Whisk together the remaining sugar and egg yolks until thick and pale, about 2 minutes. Combine the 2 cups milk and half and half in a saucepan and heat over medium-high heat until tiny bubbles form around the edge of the pan, stirring frequently. Pour 1/2 of the hot milk mixture into the egg yolk mixture, whisking constantly. Whisk in the remaining milk mixture the pour back into the saucepan. Cook over medium-low heat, stirring constantly with a wooden spoon until the mixture is thick enough to coat the back of a spoon, about 8-10 minutes. Remove from the heat and stir in the remaining 1/2 cup milk. Stir milk mixture into the blueberry mixture and chill 2 hours or up to overnight.

Remove blueberry mixture from the refrigerator and stir in the lemon juice. Pour into an ice cream maker and freeze according to manufacturers directions. Transfer to an airtight container and place in the freezer for several hours to allow ice cream to harden. Remove and let stand at room temperature 15 minute before serving.