Place 3/4 cup of the butter into a saucepan with the loose tea. Heat over medium heat until the butter melts, then reduce the heat to low and simmer for 5 minutes. Remove from the heat and let the tea steep for 5 minutes more. Strain the butter through a fine-mesh sieve set over a bowl and refrigerate it until it reaches the same consistency as softened butter (20-30 minutes). Small bits of tea may remain in the butter.
Place the egg whites and sugar in the bowl of a stand mixer. Whisk them together by hand to combine. Fill a medium saucepan with a few inches of water and place it over medium-high heat. Place the mixer bowl on top of the saucepan to create a double boiler. The bottom of the bowl should not touch the water. Whisking intermittently, heat the egg mixture until it registers 160 F (70 C) on a candy thermometer or is hot to the touch. Carefully fit the mixer bowl onto the stand mixer.
With the whisk attachment, beat the egg white mixture on high speed for 8-10 minutes, until it holds medium-stiff peaks. When done, the outside of the mixer bowl should return to room temperature and no residual heat should be escaping from the meringue out of the top of the bowl. Stop the mixer and swap out the whisk attachment for the paddle.
With the mixer on low speed, add the vanilla and salt. Next add the tea-infused butter and remaining 3/4 cup of butter a couple tablespoons at a time. Once incorporated, turn the mixer onto medium-high and beat until the buttercream is silky smooth (3-5 minutes).