Using a handheld or stand mixer fitted with a whisk attachment, beat the eggs, sugar, and lemon zest together on high speed for 8-10 minutes or until the mixture is thick, very pale, and forms ribbons when you lift the beaters. Add in the lemon extract and beat until combined.
In a small bowl, whisk together the flour, baking powder, salt, and poppy seeds. Using a spatula, gently fold the flour mixture into the egg mixture. Then gently fold the melted butter into the batter. It will take a minute or two to fully incorporate, so just keep gently mixing it together until fully combined. The batter should be thick and shinny.
Cover the bowl and let the batter chill in the fridge for 45 minutes. During the last few minutes of chilling, preheat the oven to 350°F.
Lightly brush your madeleine pan with 1-2 tablespoons of melted butter, then scoop a generous tablespoon of batter into the center of each well.
Bake for 10-12 minutes or until the madeleines are lightly browned. Transfer to a wire rack and let cool.
Whisk together the powdered sugar and lemon juice until fully combined and smooth. You may need to add an extra 1-2 teaspoons of lemon juice to reach your desired consistency.
Dip cooled madeleines in the glaze and enjoy!
Madeleines are best eaten the same day but will keep in an airtight container at room temperature for 2-3 days.