Make the cake: Preheat the oven to 350°F. Grease 2 (9x2-inch) round cake pans with cooking spray or softened butter. Line the bottoms of the pans with parchment paper and grease the parchment.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. In the bowl of a stand mixer fitted with the paddle attachment, beat the shortening, butter, and vanilla on medium to medium-high speed until fluffy and light, 2 to 3 minutes, scraping down the bowl with a rubber spatula as needed. Add the granulated sugar and continue beating for another 3 to 5 minutes, until the mixture doubles in volume.

Decrease the speed to low and add the dry ingredients in three additions, alternating with two additions of the water, scraping down the bowl as needed with a rubber spatula. Stop the mixer when there are still streaks of flour in the batter. Finish mixing by hand, adding the egg whites in three stages, and folding them in with a rubber spatula.

Transfer the batter to the prepared pans and bake for 20 to 25 minutes, rotating at the halfway point. The cakes are ready when a cake tester comes out with a few moist crumbs and the cake has just started to come away from the sides of the pan. Let cool for about 20 minutes, and invert the cakes right-side up onto cooling racks. Let the cakes cool to room temperature.

Make the buttercream: In the cleaned bowl of the stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth and soft. On low speed, slowly add the salt and 2 cups of the powdered sugar, scraping the bowl periodically with a rubber spatula. Add one-fourth of the milk and mix until incorporated. Continue mixing in this manner, adding the remaining powdered sugar and milk, until the frosting is fluffy and spreadable.

Add the vanilla and a few drops of food coloring, if using, and continue mixing on medium-low to medium speed for at least 5 minutes, until fluffy and stable. A longer mixing time results in exceptionally light frosting.

Generously frost the cooled cake layers with the buttercream, using an offset spatula or butter knife. If you do not want a thickly frosted cake, you will have leftover frosting. Sprinkle sanding sugar on top of the first frosted layer, before placing the second on top of it, and on the top and sides of the frosted cake once you are done. Slice the cake using a long serrated knife.