Preheat your oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan, or line it with parchment paper for easy removal.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, beat the softened butter and granulated sugar together. You can use an electric mixer or a whisk. Add the eggs, one at a time, beating well after each addition. Stir in the sourdough discard, lemon zest, lemon juice, vanilla extract, and milk. Mix until smooth.

Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Be careful not to overmix.

Pour the batter into the prepared loaf pan and spread it evenly.

Bake for 50-60 minutes, or until a toothpick inserted into the center of the bread comes out clean or with just a few crumbs. If the top starts to brown too quickly, cover it loosely with foil during the last 10 minutes.

Allow the bread to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.

While the bread is cooling, whisk together the powdered sugar and lemon juice to make the glaze. Adjust the consistency if needed by adding more lemon juice for a thinner glaze.

Once the bread has cooled, drizzle the lemon glaze over the top. Let it sit for a few minutes before slicing.