Add the half and half,1/2 cup of the granulated sugar, coffee beans, sea salt, and 1 cup of the heavy cream to a medium saucepan. Heat the coffee mixture over medium-low heat for3-5 minutes just until the mixture is about to boil. Remove the coffee cream from the stove and let it rest for 1 hour.
Place the egg yolks into a large bowl with the remaining granulated sugar and whisk it until it is pale yellow in color.
Place the cream and coffee mixture on the stove on medium-low heat until the mixture is heated. Gradually pour 1 cup of the coffee cream into the egg yolks, frequently whisking to prevent the eggs from coagulating.
Add the egg and coffee mixture back into the remaining cream and return it to the stove over medium-low heat. Cook the custard for 8-10 minutes, frequently stirring until the custard thickens and coats the back of your spoon.
Pour the coffee custard through a fine-mesh strainer set over a large bowl, making sure to press the coffee beans to get as much flavor as possible, then throw away the beans. Stir in the remaining cream and vanilla.
Allow the coffee custard base to cool completely before covering the custard with plastic wrap. Press the wrap directly on the surface of the coffee custard to prevent a skin from forming, then chill it overnight.
Churn the coffee ice cream base in an ice cream machine according to the manufacturer's instructions, then transfer the coffee ice cream to an airtight container and freeze for 4-6 hours.