Preheat your oven to 350°F. Grease and flour two 8-inch round cake pans.
Whisk together the all-purpose flour, granulated sugar, cocoa powder, baking powder, baking soda, and salt in a mixing bowl.
Mix in the milk, vegetable oil, Greek yogurt, eggs, and vanilla extract to the dry ingredients. Beat on medium speed until well combined.
Slowly add the boiling water to the batter and mix until combined. The batter will be thin.
Divide the batter evenly between the prepared cake pans. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool in their pans for 10 minutes before transferring them to wire racks to cool completely.
In a microwave-safe bowl, heat the chopped white chocolate and 1/4 cup of heavy cream in 30-second intervals, stirring after each, until smooth. Allow to cool slightly.
In a bowl, beat cream cheese and powdered sugar until smooth.
Add the melted white chocolate mixture to the cream cheese mixture and beat until well combined.
In a separate bowl, whip the remaining 3/4 cup of heavy cream to stiff peaks.
Gently fold the whipped cream into the white chocolate mixture until thoroughly combined.
Place one cake layer on a serving plate. Spread the white chocolate filling evenly over the top.
Place the second cake layer on top of the filling.
In a saucepan, heat 1 cup of heavy cream over medium heat until it begins to simmer.
Place the chopped semi-sweet chocolate in a bowl. Pour the hot cream over the chocolate and let it sit for 5 minutes.
Mix the chocolate and cream until smooth and glossy, then let it cool slightly.
Pour the chocolate ganache over the top of the cake, allowing it to drip down the sides.
Refrigerate the cake for at least 30 minutes to set the ganache before serving.