Combine the pitted cherries, sugar, and lemon juice in a medium heavy-bottomed saucepan. Cook over medium heat for 5 to 7 minutes, stirring occasionally, until the fruit releases plenty of juice and begins to soften. Stir the cornstarch and cool water into a smooth slurry, then add it to the cherries. Boil for 60 to 90 seconds, stirring constantly, until glossy and thick enough to leave a brief trail. Remove from the heat, stir in the almond extract, and cool completely in a shallow container.

Position a rack in the center of the oven and preheat it to 350°F (175°C). Grease three 8-inch round cake pans, line the bottoms with parchment, and lightly grease the parchment. In a large bowl, sift together the flour, cocoa powder, baking soda, baking powder, and salt. Whisk in the sugar until the mixture is evenly colored and no compact cocoa pockets remain. Proper distribution here prevents bitter cocoa streaks and uneven pockets of leavening in the baked layers.

In a second large bowl, whisk the eggs, buttermilk, oil, sour cream, and vanilla until smooth and fully blended. Add the wet mixture to the dry ingredients and whisk gently from the center outward until only a few flour streaks remain. Gradually pour in the hot coffee while whisking on low speed or by hand. The finished batter will be fluid and glossy, not thick. Scrape the bowl thoroughly, then divide about 524 grams of batter into each prepared pan for evenly sized layers.

Place the pans on the center rack with a little space between them and bake for 28 to 33 minutes, rotating their positions after 22 minutes if the oven browns unevenly. The cakes are done when the centers spring back lightly, the edges just begin pulling from the pans, and a skewer shows moist crumbs but no wet batter. An instant-read thermometer inserted in the center should register approximately 205°F to 210°F (96°C to 99°C). Avoid overbaking, which makes the thin layer edges dry first.

Set the pans on wire racks and cool the cakes in their pans for 15 minutes. Run a thin offset spatula around each edge, invert the layers onto the racks, peel away the parchment, and turn them upright. Let them cool completely for about 75 minutes before leveling or wrapping. Warm cake is fragile and releases steam, so assembling it too early can compress the crumb and melt the ganache. Once cool, trim only pronounced domes with a serrated knife, keeping the layers as even as possible.

Place the finely chopped dark chocolate in a large heatproof bowl. Heat the cream in a saucepan over medium heat until steaming and bubbling gently around the perimeter, then pour it over the chocolate. Leave it undisturbed for 3 minutes. Stir slowly from the center with a flexible spatula until dark, glossy, and completely smooth, then blend in the softened butter. Let the ganache stand at cool room temperature for 60 to 90 minutes, stirring every 15 minutes, until it holds soft peaks and spreads like thick frosting.

Place one cake layer on an 8-inch board or flat serving plate. Transfer about 200 grams of ganache to a piping bag and pipe a 1/2-inch-high border around the edge. Spread half the cooled cherry filling inside the border, keeping it level with or slightly below the ganache. Add the second cake layer and repeat with another border and the remaining filling. Set the final layer cut side down on top. Check that the stack is centered and level, adjusting it gently before the filling settles.

Spread a thin crumb coat of ganache over the top and sides with an offset spatula, filling visible gaps between the layers. Refrigerate the cake uncovered for 20 minutes, just until the coating feels firm. Apply the remaining ganache in an even layer, then refine the sides with a bench scraper while turning the cake stand. Arrange the thoroughly dried fresh cherries on top and add the chocolate shavings. Chill for at least 45 minutes to stabilize the filling, then let the cake stand at room temperature for 30 minutes before slicing.