In a heavy-bottomed saucepan, combine the eggs, sugar, and 2 pints of half & half.
Heat over low/med heat, stirring constantly so it won't scald. Heat until hot but not boiling. (It should begin coating the back of a spoon.)
Remove from heat and stir in the vanilla.
Once the vanilla is stirred in, slowly add the rest of the half & half and the cream, pouring in a slow stream and whisking vigorously to keep the mixture from curdling. *I haven't tried this, but supposedly if the mixture ends up curdling, you can pour it into a blender and blend it until smooth again. They say it might taste a tiny bit more eggy, but it doesn't affect the texture of the ice cream at all.*
Allow the ice cream mixture to cool (if you're making the ice cream later on, cover and refrigerate. Otherwise, you can place the bowl in a larger bowl full of ice water and stir the mixture to help it cool more quickly.)
When the ice cream mixture is completely cooled, follow the ice cream maker's instructions to freeze the ice cream.
Once finished in the ice cream maker, remove and place in the freezer for at least 4 hours.