In a medium saucepan, combine one cup of water and one cup of granulated sugar over medium heat. Stir until the sugar dissolves completely, then whisk in half a cup of dark cocoa powder. Bring to a gentle boil, then remove from heat and let cool.

Preheat your oven to 350°F (175°C). In a large mixing bowl, whisk together two cups of flour, one and a half cups of sugar, and one and a half cups of cocoa powder, along with baking powder, baking soda, and salt. In another bowl, combine eggs, sour cream, warm water, and vegetable oil. Gradually mix the wet into the dry ingredients until fully incorporated.

Grease and line two 9-inch round cake pans with parchment. Divide the batter and bake for 23 to 26 minutes, checking with a toothpick.

Remove cakes from the oven and let cool for 15 minutes. Invert onto wire racks and let cool completely.

In a large bowl, beat unsalted butter until creamy. Gradually incorporate cocoa powder and vanilla, then add powdered sugar and heavy cream until desired consistency. Stir in melted dark chocolate.

Place one cooled layer on a platter, brush with chocolate syrup, and add a layer of buttercream. Top with the second layer and frost the top and sides.

Chill the assembled cake in the freezer for 10 minutes if desired, then slice and serve.