Place the butter in a small saucepan over medium heat and brown it. Allow the butter to melt completely and the continue cooking, stirring the whole time, until golden flecks appear at the bottom of the pan and the mixture begins to smell warm and nutty. Do not burn the butter. Remove the mixture from heat and pour immediately into a small bowl.
In a large bowl, beat together the eggs and sugar until pale and slightly thickened, about 2-3 minutes. Add the bourbon and vanilla extract and stir to combine. Add the flour and salt and fold to combine. Add the browned butter and fold the mixture just until combined. Cover the bowl and place it in the fridge to chill for 2 hours or overnight.
When ready to make, preheat the oven to 375 degrees and melt 2 tablespoons of butter to liberally grease a madeleine pan. Spoon 1 tablespoons of batter into each madeleine pan and then bake in the preheated oven for about 13 minutes, or until the tops are puffed and the edges and bottom of each madeleine is golden. Remove from the oven and set aside to cool while you make your ganache.
For the ganache:
Warm the heavy whipping cream over the stove or in the microwave just until it’s about to boil. Remove from heat and then pour over the dark chocolate in a medium-sized bowl. Allow it to rest for 3-4 minutes. Whisk the warm cream and chocolate together until smooth. If small chunks of chocolate remain, place back in the microwave for 20 second increments until it is smooth. Stir in the bourbon.
Dip each madeleine in the ganache and then sprinkle with/dip in pecans. Set the madeleines aside on a sheet of parchment or wax paper to set. Madeleines are best eaten the day they are prepared but can be saved overnight if needed.