Combine the corn kernels, cobs and half-and-half in a medium saucepan. Place over medium heat and cook until bubbles appear at the edges of the pan; continue to cook for 8 to 10 minutes more. Remove from the heat, cover and let steep for 1 hour.
Stand the cooled cobs up in the pan. Scrape a blunt knife against each one to release any remaining liquid, then discard the cobs. Transfer the corn kernel mixture to a blender and puree until smooth.
Make the custard: Whisk together the pureed corn mixture, sugar, sour cream and vanilla in a medium saucepan and bring to a simmer over medium heat. Lightly beat the egg yolks in a medium bowl. Slowly whisk about 1/4 cup of the warm corn mixture into the beaten egg yolks, then pour into the saucepan and return to medium heat. Cook, stirring constantly with a wooden spoon, until the mixture thickens and coats the spoon, 3 to 5 minutes.
Let the custard cool slightly, then transfer to a blender, filling it only halfway (do in batches if needed). Put on the lid, leaving one corner open. Cover the lid with a kitchen towel to catch splatters and pulse until smooth. Strain the custard through a fine-mesh sieve into a large bowl; discard the solids. Repeat with any remaining custard.
Stir the mixture often until it cools to room temperature. Lightly press plastic wrap directly against the surface of the custard to prevent a skin from forming. Refrigerate until cold, about 3 hours. (For faster chilling, set the bowl of custard in a bowl of ice water and stir until cold.)
Freeze the cold custard in an ice cream maker according to the manufacturer's directions. Transfer to an airtight container and freeze until firm, 2 to 3 hours.
Scoop the ice cream into bowls. Top with caramel corn or a splash of bourbon, if desired.
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