In a saucepan, bring milk to a boil. Add tea bags and cover pot. Allow mixture to steep for 30 minutes. Discard tea bags.
Line a quarter-sheet baking pan with plastic wrap, making sure the sides of the pan are also covered. Set aside.
Pour 1 1/2 cup milk into a heavy bottomed sauce pot. Add 1/2 cup of sugar. Whisk together. Place over medium-high heat. Stir occasionally to make sure the milk does not burn along the sides or bottom of the pan. Bring to a boil.
Meanwhile, in a medium bowl whisk together egg yolks, remaining 1/4 cup sugar, cornstarch, and remaining 1/2 cup milk. Whisk until smooth.
Once milk has boiled, reduce heat. Slowly add about 1/4 cup of hot milk into cornstarch mixture. Whisk constantly to distribute the heat and temper mixture. Continue to add milk to cornstarch mixture until there are only a couple tablespoons of milk left in the pot. Pour all the egg-milk mixture back into the saucepot.
Whisk constantly over medium-low heat until the custard has thickened. Continuing mixing and let the custard come to a boil to cook out any unwanted cornstarch flavor. Remove from heat. Whisk in butter and salt until smooth.
Transfer the hot pastry cream into the prepared plastic wrapped sheet pan. Spread evenly. Cover with plastic wrap (allowing plastic wrap to touch pastry cream) and freeze for 10-15 minutes until the pastry cream has cooled to room temperature. Remove from freezer and transfer to an airtight container. Place plastic wrap directly on pastry cream to avoid condensation. Let chill in the fridge until ready to use.