Halve the vanilla beans lengthwise with a sharp knife. Scrape the seeds into a large saucepan and stir in the vanilla bean pods, cream, milk and sugar. Bring the mixture just to a boil, stirring occasionally, and remove from heat.
In a large bowl, lightly whisk the eggs. Temper the egg mixture by adding the hot cream mixture to egg mixture just ¼ cup at a time, adding the hot cream very slowly and whisking constantly. Don't add it too quickly or you'll end up with some scrambled eggs!
Once the egg mixture has warmed up a bit from the cream, pour the entire mixture back into the saucepan and cook the base over a moderately low heat, stirring constantly, until a thermometer registers 170°F. (Do not let boil).
Pour the ice cream base through a fine sieve into a clean bowl and cool. Cover the bowl and chill the ice cream base at least 6 hours, or until cold (or up to 1 day). The mixture really must be chilled well in order for the ice cream to freeze properly.
Follow the instructions for your ice cream maker to freeze the ice cream. Transfer the ice cream to an airtight container and store in the freezer to harden.