1. Combine the half-and-half and the heavy cream in a medium saucepan and bring just to a simmer over medium-high heat, taking care to prevent the liquids from boiling over.

2. Turn off the heat and immediately add the sugar and salt, stirring briefly to dissolve. Stir in the vanilla and the tea bags and let the mixture cool to room temperature, occasionally stirring and gently pressing on the tea bags to help extract their flavors. When cooled, store the mixture (including the tea bags), tightly covered, in the refrigerator overnight.

3. The following day, pass the mixture through a sieve set over a bowl, gently pushing on the tea bags to release their liquid. Tear open one of the spent tea bags; remove ¼ teaspoon of loose tea leaves, and stir them into the ice cream base. Freeze in an ice cream maker according to the manufacturer’s instructions.