Preheat your oven to 375 degrees F and line an 8x8 baking pan with parchment paper. Set aside.
In a large bowl, whisk the flour, sugar, baking soda, baking powder, and salt until combined. Add the eggs, egg white, oil, vanilla extract, and milk. Whisk the ingredients together until no dry ingredients remain, and everything is thoroughly combined. Pour the cake batter into the prepared pan.
Bake the cake for 24-26 minutes or until a toothpick comes out clean. Remove from oven and let cool completely before frosting.
To prepare the chocolate frosting, melt the chocolate in a glass bowl over a simmering bowl of water. Set aside to cool slightly.
In the bowl of your stand mixer with paddle attachment fixed, add the butter. Beat on medium speed until creamy, about 2 minutes. Add the milk and vanilla extract. Mix until combined. Gradually add the confectioner's sugar, with the mixer set on low speed. Once the confectioner's sugar has been incorporated, mix on medium-high until smooth. With the mixer once again set on low, add the melted chocolate. Mix until just combined.
Frost the cake with the chocolate frosting. Garnish with sprinkles!
NOTES: This recipe is a high-altitude cake recipe. Please see notes in blog post about cooking this cake at sea level.
