Begin by simmering (not boiling) the cream in a small saucepan with the tea bags for about 10 minutes over medium-low heat. Remove the pan from the stove, but leave the tea bags in while you work on the chocolate.
In a large microwave-safe bowl, melt the chocolate with the butter in the microwave on power level 5, microwaving for 1 minute at a time, then stirring, and repeating, until it is all melted and smooth.
Remove the tea bags from the cream and add the tea-steeped hot cream to the chocolate mixture and stir until it is smooth (if the cream was a little cold, and the mixture appears curdled, just microwave it again for a couple minutes on power level 5, stirring every minute).
Add the vanilla and salt.
Let the chocolate ganache you’ve just made sit on the counter, for an hour or so, to cool and set just enough that it is still pourable, but not super liquid (you know what I mean?).
Transfer the ganache to the tart shell using a rubber spatula, being sure to not get chocolate on the edges, and also to not disturb the delicate edges of the crust.
Let cool completely, cover, and refrigerate until the filling is set, about 4 hours and up to 8 hours before proceeding with the recipe.