Preheat the oven to 350 degrees (F).
Melt 5 tablespoons butter in saucepan over low heat. Mix in the tea. Let steep for 10 minutes.
Grease two madeleine pans with remaining butter.
In a small bowl, whisk together the coconut flour, arrowroot starch, baking soda, baking powder, salt, and xanthan gum. Set aside.
Whip the eggs until thick and lemon colored.
Strain the butter/tea mixture well - you want as much of the butter as possible. Throw away the tea.
Add the honey, melted butter, coconut milk, lemon zest, and strained butter/tea mixture into the beaten eggs, while mixing on low.
Slowly add in the dry ingredients into the wet and mix until incorporated, scraping the sides of the bowl often.
Use a cookie scoop to evenly divide the batter among the greased madeleine molds in the pans. You should fill the madeleine molds just about entirely. Do not bang the pan or pat down the batter.
Bake for 12 to 15 minutes or until a toothpick comes out clean. Mine were done in 12 minutes.
Let cool in pans for 5 minutes before turning onto a wire rack to completely cool.
*You can always use coconut oil if you are sensitive to dairy. Refined coconut oil will not have a coconut flavor.
Optional: Sprinkle the madeleines with with powdered sugar, but be aware this is not a Paleo option.