Preheat the oven to 325°F (165℃). Grease an 8.5x4.5-inch loaf pan and line with parchment paper. Set aside.
In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt.
In a large bowl, add the butter and sugar. Using a hand-held mixer, cream the butter and sugar until light and fluffy, about 2-3 minutes.Add the sourdough discard, eggs, lemon juice, vegetable oil, and lemon zest. Mix until combined.
Add the dry ingredients to the wet ingredients and mix until just combined and no dry spots remain.
Pour the batter into the prepared loaf pan and bake for 60-65 minutes or until a toothpick inserted into the center of the loaf comes out clean.Remove from the oven and let cool for 10 minutes in the pan. Then remove the loaf from the pan (you can pick up the loaf from the edges of the parchment paper) and transfer to a wire rack to cool fully.
Once the loaf has cooled, make the glaze. Combine the confectioner's sugar and lemon juice in a small bowl and whisk to combine. The glaze should be pourable, but still fairly thick (you don't want it to just run off the edges of the loaf).Pour the glaze over the cooled loaf and spread to the edges. Slice, and serve!
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Notes
To make this recipe with active sourdough starter, replace the sourdough discard with active starter (150g). You may find that your loaf cake rises a bit more than it does with the discard. If you'd like to add berries to this recipe (raspberries or blueberries would be great), try my Sourdough Lemon Raspberry Loaf Cake.