Place the milk in a medium saucepan and heat to a simmer. Pour half over the tea bags in a medium bowl and let steep for 30 minutes; strain, pressing all the liquid from the tea bags.
Stir powdered milk into remaining milk and keep warm over low heat.
Place egg yolks and sugar in a medium bowl. Using a hand mixer or whisk, beat until thick and pale yellow (the consistency of mayonnaise). While mixing, slowly add the hot milk and whisk until blended.
Stir the egg mixture back into the saucepan and add the tea-infused milk; increase heat to medium. Stir the mixture constantly with a wooden spoon, until the mixture is thickened like a custard sauce and registers 180 °F when checked with an instant-read thermometer.
Strain the custard through a fine mesh strainer into a medium bowl. Stir in cream, cover and refrigerate at least 6 hours before continuing.
Turn the machine on; pour mixture into freezer bowl, and let mix until thickened, about 20 to 25 minutes. The gelato will have a soft, creamy texture. If a firmer consistency is desired, transfer the gelato to an airtight container and place in freezer for about 2 hours. Remove from freezer about 15 minutes before serving.