Melt the butter in a small saucepan over medium low heat. Continue to cook, while stirring occasionally, until browned. Set aside and let cool slightly.
Meanwhile, heat the milk in another saucepan until steaming and small bubbles appear at the edges. Set aside and let cool slightly.
In the bowl of a stand mixer fitted with a whisk attachment or with a hand-held mixer, mix the eggs, flour, sugar, and salt until combined. While mixing on low speed, add the butter and milk slowly until incorporated. Cover and chill until ready to make crepes.
Heat a 9-inch skillet over medium heat and grease with a small amount of butter. Add approximately ⅓ cup of batter to the skillet and swirl to coat the pan evenly. Cook for a few minutes until edges begin to brown. Flip and cook for an additional minute. Repeat until the batter is gone, stacking crepes and letting them cool to room temperature.
In a medium saucepan over medium heat, bring the heavy cream to a simmer. Place the chopped dark chocolate in a medium bowl. Pour the heated heavy cream over the chocolate and let sit for 1 minute. Whisk until smooth and chill for at least 2 hours. Whip to medium peaks.
To make the cake, layer the crepes with a thin coating of chocolate ganache. Garnish cake with powdered sugar or cocoa, if desired and chill for 2 hours before serving.
Note: Cake is best the day it is made, but may be stored in the fridge for a few days.