Meanwhile, in a large bowl, with a mixer on medium speed, beat sugar and eggs. Mix in one cup of the hot cream mixture. Slowly pour egg mixture back into cream mixture in saucepan. Cook over medium heat, stirring constantly, just until mixture coats the back of a spoon (do not boil, or it will curdle). Remove saucepan from heat.
Strain custard through a sieve into a medium bowl. Remove vanilla beans; when cool enough to handle, scrape out vanilla seeds and add to custard.
Place bowl into a larger bowl filled halfway with ice water. Cool custard, stirring occasionally, until well chilled. (Or refrigerate at least 2 hours but no longer than overnight.)
Using an ice cream machine, process according to manufacturer's instructions.