Preheat oven to 350°F (175°C). Lightly grease or line an 8-inch round or square baking pan.
Make the chocolate milk mixture: In a mixing cup, combine hot milk, cocoa powder, and erythritol or stevia. Whisk until smooth. Set aside.
In a large bowl, whisk together the eggs, oil, Greek yogurt, and vanilla extract until well combined.
Add the flour, baking powder, baking soda, and salt to the wet mixture. Mix until just combined.
Pour in half of the chocolate milk mixture (save the other half for soaking). Stir until the batter is smooth and well mixed.
Pour the batter into the prepared pan. Bake for about 25–30 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool slightly in the pan.
Make the frosting: In a medium bowl, whisk together cream cheese, Greek yogurt, erythritol or stevia, and cocoa powder. Add melted dark chocolate and whisk until smooth and creamy.
Soak the cake: Use a wooden stick or skewer to poke holes all over the top of the warm cake. Slowly spoon the remaining half of the chocolate milk mixture over the cake, letting it soak in.
Spread the frosting evenly over the cake. Garnish with extra shredded dark chocolate if desired.
Refrigerate for about 30 minutes for best texture. Slice and enjoy!