Preheat your oven to 325 degrees Fahrenheit and prepare a rectangular cake pan by greasing it with butter or baking spray and lining it with parchment paper. Set it aside.
Add the flour, sugar, baking powder and salt to a large mixing bowl and whisk together until combined.
Add the shortening to the dry ingredients and using your hands or a pastry cutter, crumble the shortening together with the dry ingredients until the shortening disappears and the mixture resembles sand or fine crumbs.
Measure the milk into a liquid measuring cup and add the vanilla and the egg whites to the milk. Whisk them together well with a fork until combined.
Add the milk mixture to the dry ingredients and mix together on low speed with a hand mixer just until the mixture is smooth and no lumps remain.
Pour the batter into the prepared baking pan and bake for about 25-30 minutes at 325 degrees Fahrenheit. To see if the cake is done, insert a toothpick into the centre. If it comes out clean, the cake is done.
Place the cake pan on a wire rack to cool completely.