Set a box grater in a large bowl. Using the large holes, grate corn kernels (and their "milk") off the cobs. Discard cobs.
In a medium saucepan over medium heat, combine cream, milk, and corn. Bring to a simmer. Meanwhile, in a medium bowl, whisk sugar and egg yolks until pale and thick. When cream mixture reaches a simmer, slowly ladle 1/2 cup of it into egg mixture, whisking constantly. Repeat with another 1/2-cup ladleful. Reduce heat to low, whisk warmed egg mixture into saucepan, and cook, whisking, until mixture thickens a bit, about 5 minutes.
Pour mixture into a medium bowl, stir in vanilla, cover with plastic wrap (letting the wrap sit directly on the mixture's surface), and chill at least 2 hours and up to 1 day.
Freeze in an ice cream maker according to manufacturer's instructions. Serve immediately or transfer to an airtight plastic container and freeze up to overnight.
Note: Nutritional analysis is per serving.