In a medium pot, simmer the tea, cream, milk, sugar and salt until the sugar completely dissolves, about 5 minutes. Remove pot from heat. In a separate bowl, whisk the yolks until they're broken up.
Cool to room temperature. Strain through a fine-mesh sieve into a bowl and discard the tea bags and any scrambled egg bits that get caught in the sieve. Press out any liquid that might be held in the tea bags back into the custard. Stir in the vodka.
Ice cream adapted slightly from Melissa Clark.
You don’t need to add the alcohol, but it helps make sure the ice cream has a softer, more creamy texture.