In a medium bowl, whisk together the flour, baking powder, and salt. Set aside for later.
In the bowl of an electric mixer fitted with the whisk attachment, whip the eggs with the sugars on high speed for about 10 minutes until they are a very light cream color and thick.
Sift the dry ingredients over the mixer bowl, and fold them in with a flexible spatula, carefuly.
Add the ground tea leaves, and fold them in until they are almost, but not totally incorporated.
Mix the melted butter with the vanilla and the honey in a small cup or bowl, and pour half of it over the batter. Fold it in, then add the other half of the butter mixture. Continue folding (with a couple gentle stirs) until all the ingredients are incorporated. Make sure to scrape the sides of the bowl, and make sure that you’ve gotten all the ingredients off the bottom of the bowl.
Let the batter stand for 10 minutes. Meanwhile, prepare the pans by very generously greasing them with melted butter, brushing it into the grooves, then dust with flour, tapping out the excess.
Dollop small spoonfulls of the batter into each slot of the pan, but do not overfill. Each slot will take a generous teaspoon or so. (Practice by baking a couple if you’re unsure how much to put) Bake them for about 12 minutes, or until the edges are golden.
Immediately flip the pan over a wire rack to release all the madeleines to cool. Then re-prep the pan, and continue baking the rest of the batter.
Dust with powdered sugar just before serving, or serve them plain.