Preheat the oven to 350°F and grease a loaf pan with vegan butter or line it with parchment paper.
Melt the butter in the microwave for about 20-30 seconds or over the stovetop. Let it cool before using it. Place the plant milk and vegan yogurt on the counter so that they start to come to room temperature.
Make the vegan buttermilk by stirring together the plant milk and apple cider vinegar. Let it sit for a few minutes as it curdles.
Whisk together the flour, sugar, baking powder, cornstarch, and salt in a large bowl. Add the buttermilk, yogurt, melted butter, and vanilla to this bowl. Gently fold everything together just until it's combined. Try not to over-mix the batter.
Pour the thick batter into the loaf pan and smooth out the top with a metal spoon or spatula. Bake the cake for 45-50 minutes. It's ready when the top is slightly golden and a toothpick, inserted into the center, comes out clean.
Enjoy it right away or let it cool down before icing it. Mix the optional glaze ingredients together and spread it over the top. Let the icing set for a few minutes before slicing the cake.