Preheat oven to 325°F. Lightly butter the bottom and sides of three 8-in. round cake pans and line them with parchment paper. Set aside.

Using a double boiler positioned over simmering water, combine the egg yolks, sugar and ¼ cup of the heavy cream. Cook the mixture, whisking continuously until it thickens and turns pale, about 10 to 12 minutes. Remove the mixture from the heat.

Add the finely chopped chocolate to the egg mixture and whisk until smooth and evenly incorporated. Set aside to cool.

In the bowl of a stand mixer, combine the remaining cream with the powdered sugar and then whip the cream to stiff peaks, about 6-7 minutes.

Gradually fold the whipped cream into the chocolate mixture. Work slowly and carefully, so you don’t deflate the cream. Continue to fold the mixture together until it is evenly mixed, then cover and place it in the refrigerator for at least 2 hours or up to 2 days.

In a large mixing bowl, combine the flour, sugars, cocoa powder, baking soda, baking powder and salt. Stir and set aside.

In a separate large bowl, whisk together the Greek yogurt, oil, vanilla and eggs. Make a well in the dry ingredients and pour in the egg mixture. Stir gently until the dry ingredients are almost fully incorporated. Pour in the hot coffee and whisk it into the batter until fully incorporated.

Evenly divide the batter into the three prepared cake pans and bake for 28-32 minutes, or until the center is set and a toothpick comes out clean when inserted in the center of the cakes.

Remove the cakes from the oven and let them cool for 5-10 minutes in the pans before inverting them onto a wire rack to cool completely.

While the cakes bake and cool, prepare the frosting. Melt the butter in a saucepan. Stir occasionally and toast the butter until it begins to turn golden brown and smells fragrant. Remove from the heat.

Immediately pour the room temperature cream into the browned butter, then return the mixture to the heat. Stir until steaming, then remove from the heat. Gently stir in the chopped chocolate until melted smooth and glossy. Add the vanilla, yogurt, powdered sugar, cocoa powder and salt. Mix until evenly combined and then let cool until the frosting has thickened to a spreadable consistency, about 30-45 minutes.

Level the tops of your cake layers, brush the top with the hot chocolate soak, add the mousse between layers, and finish with the fudge frosting. Coat the tops and sides with frosting. Slice and serve.