Put the butter in a bowl and melt it in the microwave.
Open the two tea bags and pour the contents into the melted butter. Cover the bowl with a small plate and let it steep for 10 minutes.

In a bowl, mix the flour, baking powder, and salt. Set aside.
With an electric mixer, whisk together the eggs, vanilla extract, and sugar.
Add the dry ingredients and the filtered melted butter, and mix well.

Cover the bowl and refrigerate for at least 3 hours.

Drop the dough by spoonfuls into the madeleine molds and bake for 11 to 13 minutes in a preheated oven at 400°F (200°C).
Unmold and let cool on a rack.
Can be stored for about 2 months in an airtight container.