In a medium saucepan, heat cream and tea bags over medium heat until just before it boils. Reduce heat to low, and steep tea in cream for 10 minutes.
Remove tea bags from cream, squeezing excess liquid back into the pan.
Add sugar to cream, stirring well to dissolve sugar.
In the top half of a double boiler over simmering water, combine ¼ cup cream mixture with eggs. Gradually add rest of cream mixture to eggs, stirring constantly.
Cook over medium heat, stirring constantly, until mixture coats the back of a spoon, 6 to 7 minutes. Add vanilla. Strain mixture through a fine-mesh sieve into an airtight container. Cover and refrigerate for 2 hours.
Beat custard at medium-high speed with an electric mixer fitted with a whip attachment until custard begins to fluff and thicken.
In a large bowl, combine berries.
Place 1 cup mixed berries in each of 8 dessert dishes. Top each with 1 cup whipped custard. Top with remainder of berry mixture and orange zest.