Preheat the oven to 350°F.
Lightly coat a 9x9-inch baking pan with nonstick baking spray.
Set the prepared pan aside.
In a medium bowl, combine the all-purpose flour and baking powder.
Stir until evenly mixed, then set aside.
Add the room-temperature eggs to the bowl of a stand mixer.
Beat the eggs on high speed for 3 to 4 minutes, or until thick, pale, and airy.
Gradually add the sugar to the beaten eggs.
Continue mixing on medium speed for 4 to 5 minutes, or until the mixture is light and fluffy.
Gradually add the flour and baking powder mixture to the egg mixture.
Mix on medium speed until the batter is smooth and fully combined.
In a small saucepan, combine the milk and butter.
Heat over medium-low heat until the butter is melted and the milk is hot.
Slowly add the hot milk and butter mixture to the cake batter.
Mix until fully incorporated.
Pour the batter into the prepared baking pan.
Spread the batter evenly.
Bake for 20 to 25 minutes, or until the cake is lightly golden and a toothpick inserted into the center comes out clean.
Remove the cake from the oven.
Place the pan on a cooling rack.
Allow the cake to cool completely before frosting.
To prepare the chocolate ganache, place the chocolate chips in a medium heat-safe bowl.
Heat the cream in the microwave for approximately 90 seconds, or until it is just about to boil.
Pour the hot cream over the chocolate chips.
Cover the bowl with a plate and allow it to sit for 1 minute.
Stir until the chocolate is fully melted and the ganache is smooth and glossy.
Add the vanilla extract.
Stir until combined.
Spread the chocolate ganache evenly over the cooled cake.
Allow the ganache to set slightly before slicing.
Dust with powdered sugar, if desired.
Slice and serve.