Lacking emulsified shortening, it's necessary to provide emulsifiers from somewhere else. Egg yolks are good choice.
Here's what I do: (This makes one 1.5" by 9" cake, or one not-quite 2"X8", and scales to enough to make a full sheet, by simple multiplication). (Forgive the rather bizarre mixed units.)
Sugar 6 oz
Cake flour 4 oz
Cocoa powder (undutched) 1 1/3 oz
baking powder 2 g
baking soda 2 g
salt 1g
milk 3 fl oz
eggs 4oz (feel free to round that up to nearest whole egg, it works fine)
light corn syrup 1 oz
vanilla extract 1 teaspoon
butter 4 oz (you can use solid shortening, but butter tastes better)
Sift together dry ingredients
mix liquids together and whisk together
Blend the butter, dry ingredients and about half the liquid with a mixer (stand or hand works fine) at a medium speed for about 3 minutes (scrapping the bowl as required)
Add half the remaining liquid, blend 90 seconds to two minutes longer
Add rest of liquid, blend 90 to 120 seconds.
Bake at 350, until done (tooth pick in center is clean is fine test for this), about 30 minutes.
Cool in pan a few minutes, then transfer to rack to cool completely.
If you're making a layer cake, you can moisten the layers wit h a simple syrup solution. You can use a plain one, or flavor it in a way that complements (or contrasts with) the filling or frosting. (I just did this cake, with a raspberry syrup, stabilized whipped cream filling, and mint flavored chocolate ganache frosting. It went over quite well.)