In a clean bowl of a stand mixer fitted with a clean whisk attachment, beat yolks at medium speed until they become light and lemony in color and ribbons form when the whisk is lifted, about 5 minutes.
Meanwhile, in a small saucepan, combine the sugar and water. Cook over medium-low heat, swirling pan occasionally, until the sugar completely dissolves and the syrup comes just to a boil. Increase the heat to high and boil syrup until it registers 238°F on a candy thermometer. With the mixer on medium speed, carefully add the hot syrup to the egg yolks in a thin, steady stream. Beat the mixture until it cools to room temperature and is light and fluffy, about 10 minutes. Gradually add the butter a tablespoon at a time until completely incorporated. In a small bowl, dissolve the espresso powder in the Kahlùa (or water); beat into the buttercream.
Invert cake onto a large wire rack and peel off the parchment paper. Invert cake again onto a large cutting board. With a serrated knife, cut the cake equally into thirds. Set a large wire rack over a baking sheet (this will collect the poured ganache). Arrange one cake layer on rack; spread half the buttercream evenly over top. Add another cake layer and spread remaining buttercream on top. Place the remaining cake layer over buttercream. Place the cake in the refrigerator for at least 30 minutes to set and chill slightly.
Meanwhile, in a large bowl, combine the chocolate and butter. In a small saucepan, heat cream and sugar over medium-high heat, stirring occasionally until small bubbles appear around the edge of the pan. Pour the hot cream mixture of the chocolate and butter; stir until the mixture is completely melted and smooth. Cool, stirring occasionally, until it is thickened and cooled, but not pasty, about 20 minutes.
Remove the cake from the refrigerator and pour the ganache over the top of the cake, spreading with an off-set spatula so it coats the sides. If ganache does not cover the sides completely, pour any excess that has collected on the baking sheet back into the bowl and spread again. Refrigerate the cake until the ganache sets, at least 1 hour. Using two large spatulas, carefully transfer the cake onto a serving platter. Leftover cake can be stored in the refrigerator, covered for up to five days. Set the cake out at room temperature for 30 minutes before serving. Enjoy!