Preheat oven to 350 F and butter a 9 x 13 inch pan. Dust with flour. Add all ingredients except the shredded potato into the bowl of a stand mixer fitted with a paddle attachment (or a large mixing bowl in which you’ll use hand beaters).
Turn on the mixer and beat for 2-3 minutes until batter is well-combined and silky. Add the shredded potato and stir in with a wooden spoon. Transfer mixture to prepared pan.
Bake until tester comes out clean, 35-40 minutes. Cool cake in pan on a wire rack before inverting and preparing to frost.
Make the frosting: Using the whisk attachment on a stand mixer (or traditional beaters), beat all frosting ingredients together until smooth, about two minutes.
Note: If you don’t finish it all in one evening, wrap with plastic wrap and leave room temperature for up to three days. The frosting will firm up quite a bit in the refrigerator, so if you’d prefer to store it there that’s fine as well.