In a large sized mixing bowl, whisk together the granulated sugar, milk, sourdough discard, eggs, and vanilla extract. Set aside.
In a medium mixing bowl, whisk together the flour, baking powder, baking soda, and salt.
To the flour mixture, add in the soft room temperature butter. Using your fingers, two forks, or a pastry blender, cut in the butter until it resembles coarse sand, with some pea sized butter remaining.
Add the flour/butter mixture to the large mixing bowl. Using a hand held electric mixer, mix, mix for 3-5 minutes, until the batter is mostly lump free. Start on low speed and gradually work your way up to medium speed.
Pour into the prepared 9x13 pan and spread out so the batter is even in the pan.
Bake for 30-35 minutes, or until the cake is golden brown on top and a toothpick inserted into the center of the cake comes out clean.
Allow to cool in the pan completely.
Frosting the cake
In a medium mixing bowl, mix the room temperature butter with a handheld electric mixer until the butter is soft and fluffy.
Add in the powdered sugar and mix to combine. I recommend starting with just ½ cup and mixing that, and then adding 1 cup, mixing, and then adding the final cup and mixing. That way the butter can slowly absorb the sugar and the sugar won’t fly all over your kitchen.
Add in the vanilla extract, pinch of salt, and ¼ cup of milk. Mix until smooth.
Taste and adjust for your preferences. If you want your frosting to be thicker, add a little more powdered sugar. If you want the frosting to be thinner and softer, add a splash more of milk.
Frost and decorate the cake as desired.
Notes
Cake can be stored in a covered container at room temperature for up to 4 days, or up to a week in the refrigerator.