Step 1: Melt the butter in a small saucepan over medium heat, stirring occasionally until it browns and smells nutty. Remove from heat and stir in the honey. Let it cool to lukewarm.
Step 2: In a large bowl, whisk the eggs and sugar together for about 5 minutes until pale and thick. Sift in the flour, matcha powder, baking powder, and salt.
Step 3: Gently fold the dry ingredients into the egg mixture until just combined. Gradually stream in the browned butter while folding gently until smooth.
Step 4: Cover the bowl and refrigerate the batter for at least 2 hours. This step is essential for the classic madeleine hump.
Step 5: Preheat your oven to 400°F (200°C) and grease a madeleine pan. Spoon the cold batter into the molds and bake for 8-10 minutes until the centers have risen and the edges are firm.
Step 6: Remove from the oven and tap the pan against the counter to release the cakes. Cool on a wire rack.