Preheat oven to 350°F. Prep a 9x13-inch baking dish with baking spray. Separate the egg yolks from the egg whites and set aside.
In a large bowl of a stand mixer, beat ¾ cup of the sugar with the egg yolks on medium-high until creamy and light. Add the milk and vanilla and beat again, scraping down the sides of the bowl as needed.
Add the flour, cocoa powder, baking powder, baking soda, and salt, mixing just until combined.
Whisk the eggs whites, gradually adding the remaining ¼ cup of sugar until stiff peaks form. Fold into the cake batter.
Pour into the prepared pan.
Bake for 25-30 minutes. Cool completely, then poke all over with a fork.
In a separate bowl, whisk together the cocoa powder, sweetened condensed milk, evaporated milk, and milk. Pour over the cooled cake. Let soak for at least 3 hours or overnight in the fridge.
Whip the cream, cocoa powder, sugar, and vanilla, then spread over the cake. Sprinkle with semi-sweet chocolate curls, slice, and serve.