Preparation

1. Preheat oven to 300°F. Brush a 9x3-inch round cake pan with melted unsalted butter. Line bottom with a 9-inch round of parchment paper and brush parchment with melted butter.
2. Place water, granulated sugar, ¼ cup of the brown sugar, and espresso powder in a 2½-quart saucepan. Bring to a simmer over medium heat and cook until sugars are dissolved. 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. Let cool while continuing.
3. Place eggs and remaining ¼ cup brown sugar in the Cuisinart™ mixing bowl. Insert flat mixing paddle. Set timer for 12 minutes and mix on speed 10 until thickened and light, similar to mayonnaise in texture. With the stand mixer set on speed 2, add the slightly cooled chocolate mixture in a steady stream, and mix for 1 minute. Scrape the bowl and paddle. 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.
4. Transfer to 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.
5. Let cool at room temperature, then cover and refrigerate for 8 hours or overnight.
6. 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.