Prepare: Preheat your oven to 175°C (350°F). Lightly grease an 8" loaf tin and place a sling of parchment paper into it to help lift out the cake once baked.
To make the vegan "buttermilk" add the soy milk and lemon juice to a small bowl, stir and allow to sit for 10 minutes.
Add the sugar, lemon zest, and scraped-out seeds from the vanilla pod to a large mixing bowl. Use your fingertips to rub the zest into the sugar.
Add the melted butter and whisk to combine. Add in the olive oil and yogurt and whisk for a minute until everything is combined. Then add the vegan buttermilk mixture, and whisk again.
Add the sifted flour, baking powder, baking soda, and salt to the bowl with the wet ingredients and fold with a spatula until just combined and there aren't any visible pockets of flour - be careful not to overmix the batter.
Bake: Transfer the cake batter to the prepared loaf pan. Cut thin strips of vegan butter and place them down the center of the loaf, this will help the loaf to crack in the center once it bakes (*see notes). Bake for 40-45 mins. Check the cake is ready by inserting a knife or toothpick into it, which should come out clean. Allow the cake to cool in the pan for about 10 minutes before transferring it to a cooling rack to cool completely.
Make the glaze: Meanwhile, add the powdered sugar, lemon juice, and yogurt to a bowl and whisk until smooth.
Once the cake has cooled, place a sheet of parchment paper under the cooling rack to catch any icing. Pour the glaze on top of the cake, and smooth it over the sides so that it covers the entire surface. You can eat the cake as is, or allow the icing to set for an hour or so before serving.
Storage: Store in an airtight container at room temperature for up to 5 days, or in the fridge for up to a week. You can also freeze this cake in an airtight container and defrost it a couple of hours before serving.
