In a large bowl, beat the eggs and sugar until well whipped, thickened, and a pale yellow color, 5-10 minutes. Whisk in the vanille extract.
In a medium bowl, whisk together the flour, hojicha powder, baking powder, and salt.
Pour half of the flour mixture into the beaten eggs and gently fold until just combined with no streaks. Add the remainder of the flour and gently fold, taking care not to deflate the mixture.
Gently fold half of the melted butter into the batter until just combined, then fold in the remainder until all the butter has been incorporated.
Cover the bowl and refrigerate for 30 minutes to 1 hour.
Preheat oven to 425˚F (220˚F). Grease the cavities of a madeleine pan well with butter.
Place a spoonful of batter into the center of each cavity. Do not spread it out. Each cavity should be about 3/4 full. Refrigerate remaining batter between batches.
Place the pan in the preheated oven and immediately reduce heat to 400˚F (200˚C). Bake until the edges are starting to turn golden and the batter has puffed and set, 10-12 minutes. Do not open the oven door until nearly done. Allow the madeleines to cool in the pan for 5 minutes before transferring to a wire rack. Clean the pan, grease, and repeat with remaining batter.
The madeleines are best served within a couple of hours of baking. Sprinkle with powdered sugar, if desired. Store cooled madeleines in an airtight container at room temperature for up to 1 day.