Combine corn and half-and-half in a food processor; process until smooth (about 1 minute). Pour pureed corn mixture into a sieve over a large bowl, reserving liquid; discard solids. Add 2 cups milk, sugar, salt, and egg yolks; stir with a whisk. Pour mixture into a large saucepan; cook over medium heat until thick (do not boil), stirring constantly (about 20 minutes). Remove from heat. Place pan in a large ice-filled bowl for 30 minutes or until mixture comes to room temperature, stirring occasionally.
Combine 3 tablespoons milk and caramels in a small saucepan. Bring to a simmer; cook 10 minutes or until caramels melt, stirring frequently. Remove from heat; whisk until smooth. Cool slightly.
Pour corn mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Stir in caramel mixture. Spoon ice cream into a freezer-safe container; cover and freeze 2 hours.