Slice the kernels from the cob with a knife and place them in a large saucepan.
Cut or break the cobs into thirds and add them to the pot with milk, cream, and 1/2 cup of sugar. Bring mixture to a boil, stirring occasionally. Turn off the heat and allow the mixture to sit for 10 minutes. Remove the cobs, and discard them. Puree the mixture in a blender until smooth. Return the blended mixture to the pot and allow it to sit covered for 1 hour.
Uncover the pot and bring the mixture to a simmer over medium-low heat. Simmer for about 5 minutes and turn off the heat.
In a small bowl, whisk the egg yolks and the remaining 1/4 cup of sugar. Add a cup of the hot cream mixture to the yolks while stirring vigorously to prevent the yolks from curdling. Next, stir in the yolk mixture into the saucepan. Cook over medium-low heat, stirring constantly, until the mixture is thick enough to coat the back of a spoon, about 10 minutes.
Remove from heat and strain the mixture through a sieve pressing down on the solids. Strain the mixture once again through a fine sieve into a medium mixing bowl. Fill a larger bowl halfway with very icy water and nestle the medium bowl inside. Stir frequently until the mixture is cold. Pour the mixture into an ice cream maker and process according to the manufacturer’s instructions.
Cover and chill in the fridge for at least 4 hours or overnight. When the ice cream is frozen, layer about a third of it into a container. Drizzle about 2 tablespoons of caramel on top of the ice cream, then repeat again two more times. You will have leftover caramel.
Use a knife or chopsticks to swirl the ice cream. If you prefer softer ice cream, eat it right away or freeze for about 4 hours before serving.