Preheat the oven to 350°F (175°C). Grease and flour two 9-inch (23 cm) round cake pans and line the bottoms with parchment paper.
In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt until well combined.
Add the eggs, milk, vegetable oil, and vanilla extract to the dry ingredients. Beat on medium speed with an electric mixer for 2 minutes until smooth.
Carefully stir in the boiling water. The batter will be thin, but this is normal.
Divide the batter evenly between the prepared cake pans.
Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes.
Run a knife around the edges to loosen the cakes, then invert onto wire racks to cool completely.
To prepare the chocolate ganache, place the chopped semisweet chocolate in a heatproof bowl.
Heat the heavy cream in a small saucepan over medium heat until it just begins to simmer. Do not boil.
Pour the hot cream over the chopped chocolate and let sit for 5 minutes.
Stir gently until the chocolate is completely melted and the ganache is smooth.
Allow the ganache to cool at room temperature until it thickens to a spreadable consistency, about 30 minutes.
Place one cake layer on a serving plate and spread a layer of ganache over the top.
Place the second cake layer on top and spread the remaining ganache evenly over the top and sides of the cake.
Let the cake set for 15 minutes before slicing and serving.