Make the brown butter: In a small saucepan, melt the butter over medium heat. Once melted, stir frequently and watch closely for the formation of brown specs on the bottom of the pan and a nutty aroma. Once you see brown specs, stir for just a few more seconds (it browns super quickly). Remove from the heat and immediately pour into a different bowl to prevent it from burning. Let the butter cool slightly (5-10 minutes) before using.
Using a handheld or stand mixer fitted with a whisk attachment, beat the eggs and sugar 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 vanilla extract and bourbon and beat until combined.
In a small bowl, whisk together the flour, almond flour, baking powder, and salt.
Using a spatula, gently fold the flour mixture into the egg mixture. Then gently fold the brown 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 all of the glaze ingredients until fully combined and smooth. You may need to add an extra 1-2 teaspoons of milk or cream to reach your desired consistency.
Dip cooled madeleines in the glaze and top with chopped pecans.
Notes
Madeleines are best eaten the same day but will keep in an airtight container at room temperature for 2-3 days.