In a large bowl, combine flour, baking powder, salt, and matcha powder, whisking to combine thoroughly. In another bowl, mix together the eggs, milk, and sugar. Gently fold the wet ingredients into the dry ones, adding the melted butter, until combined.
Chill the batter in the refrigerator for 1-3 hours.
After chilling, preheat oven to 375 degrees. Brush the madeleine pan with some melted butter and add a light dusting of flour. Add the madeleine batter to the pan (either using a scoop or piping bag). Don’t worry about it being uneven- it will even out while it cooks.
Cook in oven for 11-12 minutes just until the edges start to turn golden (if you cook for longer, you run the risk of them turning brown instead of green). Let them cool on a cooling rack.
Meanwhile, make the glaze by combining 1 tbsp lime juice, the zest from 1 lime, the powdered sugar, and the matcha (you can change the consistency by adding a few tsp milk or extra powdered sugar until it reaches the desired consistency).
When the madeleines are sufficiently cooled, dip each one partially into the glaze and then partially into the crushed pistachios.