In a medium bowl, whisk together the flour, almond meal, baking powder, and salt.
In another medium bowl, combine the melted brown butter, lemon zest, lemon extract, and honey. Allow to cool slightly while mixing the eggs.
In a stand mixer fitted with the whisk attachment, whip the eggs and superfine sugar on medium-high speed for about 4 minutes, until thick, foamy, and light in color. Turn the speed to medium-low and slowly add the browned butter mixture. Fold in the flour, mixing until just combined.
Cover and refrigerate until well chilled, at least two hours, but overnight is best. You can let it sit in the refrigerator for up to 3 days.
Preheat the oven to 375°F / 190°C. Brush the wells of a madeleine pan generously with softened butter and dust with flour, tapping out the excess so there is just a thin coating in the pan, or coat with beeswax.
Using a #50 (4-teaspoon) portion scoop, fill each well three-quarters full of batter. Using wet fingers, flatten the batter. Place the pan in the freezer for about 10 minutes. The batter should be stiff but not frozen solid.
Bake in the middle of the oven for 10 to 12 minutes, until the edges are a caramel color and the centers are puffed and set. Let the madeleines cool for a minute. Then remove them from the pan by flipping the pan over and gently tapping. If they stick, use a small metal spatula to ease them out of the pan. Let cool completely on a cooling rack. If you are baking multiple batches, you will need to wipe the pan clean and reapply the butter and flour. The madeleines are best eaten the same day.