Preheat the oven to 350 degrees F (175 degrees C). Line two 24-cup mini muffin pans with paper liners.

Place butter and chocolate in a heatproof bowl set over a saucepan of simmering water. Make sure the bowl isn't touching the water. Whisk until melted and smooth, about 5 minutes. Remove bowl; keep water simmering in the saucepan.

Whisk sugar and flour together in another bowl. Mix into the melted chocolate mixture. Add eggs one at a time, then whisk vanilla extract into the batter.

Divide batter among the prepared cups, filling each 3/4 of the way.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 15 to 18 minutes. Remove from the pans and cool on a wire rack, at least 20 minutes.

While cupcakes are cooling, make the icing. Use a whisk to combine sugar, egg whites, lemon juice, and salt in the bowl of a stand mixer. Empty tea bags and add loose tea to the bowl.

Set the bowl over the saucepan of simmering water; whisk until the mixture is hot and the sugar dissolves, about 2 minutes.

Transfer the bowl to the stand mixer and lock the whisk attachment in place. Beat on medium-high speed until frosting holds stiff peaks, about 7 minutes.

Transfer frosting to a large resealable plastic bag. Snip off 1 corner and pipe over the cooled cupcakes.