In a microwave-safe bowl, melt chocolate chips in the microwave for 20 seconds at a time, until soft. Stir until smooth. Stir in ¼ cup sugar and 1/4 cup hot water until well blended and lump-free. Let cool. Line the bottom of two 9x13 baking pans with parchment paper.
Preheat oven to 350 F. In a large bowl, combine the flour, baking powder, salt, baking soda and 1 and ½ cups of sugar. In another bowl. Whisk together the egg yolks, water, oil, and vanilla. Add the flour mixture to the yolk mixture and beat with a hand whisk until smooth.
In a bowl of a stand mixer with clean beaters, beat egg whites until frothy. Add lemon juice and continue to beat on high speed until stiff peaks form. Fold the egg whites into the yolk batter gradually until no white streaks remain. Pour 1/2 of the batter into another bowl. To one bowl of the batter, gradually fold the chocolate mixture until well combined.
Pour each batter into the prepared baking pans. Swirl the pans around to distribute the batters into the corners and sides of the pans. Bake at 350 F for 15 minutes, or until a toothpick inserted into the center of the cakes come out clean. Depending on how equally you divided the batters, one pan may need to bake a few minutes more than the other.
Let the cakes cool for about ten minutes until the pans are warm enough to handle. Slide the cakes into wire racks, including the parchment paper backing. Let them cool completely. Meanwhile, make the vanilla buttercream (instruction below).
Remove the parchment backing of the cakes. To do this, sprinkle some powdered sugar on top of the cakes. Top each of the cakes with a piece of parchment paper that is about the same as their sizes. Top them with a baking pan that have the same size as well. Invert the pans over, and carefully peel off the parchment paper. Repeat the same procedure to turn the cakes over again so that they are facing up once again. The cakes should be resting on inverted baking pans.
Spread the buttercream on the surface of the denser/heavier cake. To me, its always the chocolate. Carefully lift the other cake and position it over the frosted cake, face down. Trim the edges if desired, for a clean cut along the edges.
Using a sharp knife, slice the cake into seven portions horizontally. Then, slice the cake in half vertically, yielding 14 equal rectangle cake slices. Serve the cake slices on a platter, or wrap them individually.
In a small bowl, whisk the softened butter until fluffy. Add the milk, powdered sugar, and vanilla. Stir until smooth. To adjust the consistency, add a bit more sugar or milk. You want a nice spreadable consistency.
Recipe for the chiffon cake based here.