1. Preheat the oven to 325°. Grease a 10-inch springform pan, line with a circle of parchment paper and lightly grease the paper. Combine the butter, both chocolates and coffee in the top of a double boiler or a stainless steel or glass bowl. Set the bowl or insert over a pot of barely simmering water and stir frequently with a wooden spoon until melted. If the melted mixture appears somewhat speckled with what looks like unmelted chocolate, don’t be concerned. (Different chocolates have different cocoa butter and cocoa solids content and when melted with such a large quantity of liquid may seem to separate.) Place the sugar in the bottom of a large mixing bowl, or the bowl of an electric mixer. Remove the chocolate mixture from the heat and pour over the sugar. Stir to blend and dissolve the sugar, then allow to cool for 10 minutes.
2. With a wire whisk or the paddle attachment of an electric mixer, add the Kahlúa and vanilla extract to the cooled chocolate mixture and blend well. Blend in the lightly beaten eggs, making sure they are thoroughly incorporated. The batter at this point will be extremely thin; don’t worry, just make sure to work each added ingredient into it carefully.
3. Sift the flours, baking soda and salt together. Add dry ingredients to the chocolate mixture in two additions, scraping down the sides of the bowl several times. Beat on medium speed for one minute. The batter may have little lumps, but they won’t affect the finished cake.
4. Place the prepared pan on a baking sheet to catch any leaks and pour the batter into the pan. Bake in the middle of the oven for 1¾ hours to 2 hours, rotating the pan several times during that time to ensure even baking. The cake bakes slowly and stays beautifully moist. A crust will form on the top of the cake and may crack. Test for doneness by inserting a wooden skewer in a fault of the crust, poking near the centre of the cake. It should come out clean, or with only a very few moist crumbs clinging to it. Remove the cake from the oven and cool completely in the pan set on a rack. (The cake may be made up to 2 days ahead of time and kept in the pan at room temperature, covered tightly with plastic wrap.)
5. To prepare the glaze, combine the chopped chocolate and butter in the top of a double boiler or a bowl set over barely simmering water. Stir frequently until melted, then remove from the heat and cool slightly, stirring occasionally. Run a thin-bladed knife around the cake and loosen and remove the sides of the pan. Using a long-bladed serrated knife, carefully even out the top of the cake, slicing off any domed or uneven part of the crust. Use long, slow strokes of the knife, keeping the blade perfectly parallel with the counter.
6. Place a dab of the chocolate glaze on a 10-inch cardboard cake circle and invert the cake onto the board. Remove the pan bottom and the parchment paper. (If you haven’t got a cake circle or other piece of cardboard cut to 10 inches round, invert the cake onto a plate and remove the pan bottom but leave the paper. Re-invert the cake onto a second plate and place the pan bottom on the top of the cake. Invert the cake a third time, ending up with the bottom-side up, top-side down on the metal pan bottom, and peel off the paper.) Brush any crumbs from the cake and pour the warm glaze onto the centre. Using a metal spatula or palette knife, coax the glaze to the edges of the cake and over the sides; quickly spread the overflow evenly onto the sides. Garnish with the chocolate-covered espresso beans. Give the glaze an hour or so to set, then serve the cake with lightly sweetened whipped cream, if desired.