Slice kernels off corncobs and add to the bowl of a food processor or blender. Add milk and process until pureed. Add puree and cream to a large saucepan over high heat. Break cobs into large pieces and add to the saucepan with ½ cup sugar. Once mixture boils, stir and remove from heat. Cover pan and let sit 1 hour.

Discard cobs and bring mixture to a simmer over medium heat. Meanwhile, whisk egg yolks and remaining ¼ cup sugar together in a medium bowl. Add 1 cup of the hot liquid to the yolk mixture and whisk until combined. Add yolk mixture to the hot liquid, whisking until combined. Reduce heat to medium-low and cook until custard thickens and coats the back of a spoon, about 10 minutes.

Strain custard through a fine-mesh sieve and discard solids. Let custard cool to room temperature. Chill in the refrigerator for at least 4 hours. Freeze in an ice cream maker according to manufacturer’s instructions. About halfway through churning, add salt. Finish churning, then transfer to a lidded container, cover, and freeze for at least 2 hours. Soften at room temperature for at least 5 minutes before serving.