Cut open the tea bags and empty them into a saucepan. Add the half-and-half and bring almost to a simmer, whisking constantly. Continue steeping, while maintaining the heat for 20 minutes, or until the cream is the colour of a latte, or deep beige.
Meanwhile, whisk together the yolks, sugar, and salt in a large mixing bowl.
Stir the mixture over medium heat or until thickened.
Allow to cool to room temperature, cover, and chill in the fridge completely, preferably overnight.
Churn in an ice cream according to manufacturer's instructions. Transfer to a freezable container and freeze until firm.