Preheat oven to 350 degrees F (175 degrees C). Butter a 7-inch cake pan.
Beat shortening and sugar together in a large bowl with an electric mixer until light and fluffy; add eggs one at a time, thoroughly beating each egg into the batter before adding the next. Add vanilla extract and fold orange zest into batter. Mix flour into batter until just incorporated. Pour batter into prepared cake pan.
Bake in the preheated oven until golden brown and a toothpick inserted into the center of the cake comes out clean, about 25 minutes. Cool in the pan for 10 minutes before transferring to a wire rack to cool completely.