Preparation

1. Preheat oven to 300°F. Brush a 9x3-inch round cake pan with the melted butter. Line the bottom of the pan with a round of parchment paper and brush parchment with additional melted butter.
2. Put the water, granulated sugar, ¼ cup of the brown sugar, and espresso powder in a medium saucepan. Bring to a simmer over medium heat and cook until sugars are dissolved.
3. Reduce heat to low. Add all chopped chocolate and stir with a wooden spoon until smooth. Remove from heat and add half the butter; stir until smooth. Add remaining butter, vanilla, and liqueur or brandy; stir until smooth. Cool to room temperature.
4. While the chocolate/butter mixture is cooling, prepare the rest of the cake batter. Put the eggs and remaining ¼ cup brown sugar in the mixing bowl. Insert whisk. Mix on speed 10 until thickened and light, similar to mayonnaise in texture; this could take up to 10 minutes. With the stand mixer set on speed 2, add the cooled chocolate mixture in a steady stream, and mix for 1 minute. Scrape the bowl and whisk.
5. Remove the bowl from the stand mixer. Using a large rubber spatula, gently fold until the mixture is completely homogenous in color, with no streaks of chocolate or egg – be gentle, taking care not to deflate the egg mixture to much.
6. Transfer to the prepared pan. Place filled cake pan in a larger pan and add hot water so that it is halfway up the sides of the cake pan. Place in preheated 300°F oven and bake for 1 hour 20 minutes. Cake should rise evenly, and when done, the top will have the appearance of brownies, but the cake will still seem a little jiggly.
7. Let cool at room temperature, then cover and refrigerate for 8 hours or overnight.
8. To unmold, dip the bottom of the cake pan in hot water for 10 to 15 seconds. Dry pan and invert cake onto a serving platter. Remove parchment. Dust with powdered sugar before serving, or top with Chocolate Glaze. Smooth chocolate glaze over top with a minimum of strokes to keep its shine and allow to drip down the sides of the cake.