Preheat the oven to 350°F/180°C and line an 8x4-inch or 9x5-inch loaf pan with parchment paper and lightly grease. Set the oven racks to the middle or lower third of the oven.
Make the batter. In a large mixing bowl, whisk together the wet ingredients of the plant based milk, oil, vegan yogurt, sugar, vanilla extract, and lemon zest. Into the same bowl, sift together the flour, cornstarch, baking powder, baking soda, salt, and poppyseeds. Switch to a spatula and mix to combine. The batter is very thick so try to avoid overmixing.
Place batter in pan. Using a large spoon, spread or pour the batter into the prepared cake pan. Take a butter knife and run a line through the long ways of the cake to provide a perforation in the cake batter for best rise.
Bake the cake. Bake uncovered for 60 to 65 minutes, depending on the size and type of loaf pan you are using. An 8x4-inch cake will take 55 to 65 minutes and a 9x5-inch cake will take 60 to 65 minutes. If the cake is browning too quickly, tent with foil half way through baking. Bake times can vary, so please pay attention to the cake as it bakes and don’t be alarmed if your cake takes a few minutes longer. The cake is done when a toothpick inserted into the cake pulls out mostly clean. A few crumbs on the toothpick are okay.
Cooling the cake. Remove the cake from the oven and place on a wire rack to cool in the hot pan for a minimum of 45 minutes. Then, carefully remove the still warm cake from the pan to either cool completely or frost with icing.
Make the Icing. In a small bowl, whisk together the powdered sugar, vanilla extract, and lemon juice. Pour over top of the cake and serve. Enjoy!