Place one cup of the butter in a saucepan with the loose tea. Heat until the butter melts, then reduce heat to low and simmer for 5 minutes.
Remove from heat and let steep for 5 minutes more.
Strain the butter and then refrigerate it until it cools to the consistency of softened butter. About 30 minutes.
Place the egg whites and sugar in the bowl of a stand mixer and whisk by hand to combine.
Fill a saucepan with a few inches of water and place it over medium heat. Place the mixer bowl on top of the saucepan to create a double boiler. Whisk intermittently, and heat the egg mixture until it reaches 160 F.
Place the mixer bowl back onto the stand mixer.
With the whisk attachment beat the egg mixture for 10 minutes, until it holds medium stiff peaks.
Stop the mixture and change to the paddle attachment.
With mixture on low speed, add the vanilla, tea infused butter, and remaining one cup of butter, a tablespoon at a time.
Once all incorporated, mix until the buttercream is silky smooth, about 5 minutes.
Spread buttercream between layers and lightly on top and sides of cake.
Refrigerate until set, about 30 minutes.
Pour caramel drizzle onto cake.