Combine the cream, milk, sugar, salt, corn kernels, and cobs in a saucepan. Heat until steaming, about 5 minutes. Cover and steep 30 minutes off heat.

Remove cobs. Whisk egg yolks in a bowl. Temper with 1 cup hot milk, then return to pan. Cook over medium-low, stirring, until custard coats the back of a spoon and reaches 170°F (77°C), about 10 to 15 minutes.

Strain custard through a fine-mesh sieve, stir in vanilla, and cool over an ice bath 10 minutes. Refrigerate until very cold, at least 4 hours or overnight.

Churn in ice cream maker until soft-serve consistency, 20 to 25 minutes.

Transfer to a container, press plastic wrap on surface, and freeze until firm, at least 4 hours. Let soften a few minutes, then scoop and serve.