In a small saucepan, warm the milk, half and half, and sugar over medium-heat, stirring occasionally. Once the milk is steaming (but not boiling), remove pan from heat. Place the tea bags into the pan, cover and steep at room temperature for 15-20 minutes, stirring occasionally. Remove tea bags, then return to medium-heat.

Meanwhile, in a separate bowl, whisk together the egg yolks and vanilla until frothy. Once the milk mixture is re-warmed, add 2 Tbsp. of the hot milk mixture to the eggs, and quickly whisk in until combined. Repeat 2-3 more times with more of the milk mixture, then gradually pour in the remainder of the milk mixture into the egg yolks and whisk quickly until combined.

Return the new milk/egg mixture to the saucepan, and cook over medium heat, stirring and scrapping the bottom of the pan constantly until the mixture thickens to a custard and coats the back of a wooden spoon.

Immediately strain through a fine-mesh strainer, and then refrigerate until completely cooled (at least 6-8 hours). Then freeze with an ice cream maker according to manufacturer's instructions.