Preheat the oven to 350 degrees F. Grease and lightly flour a loaf pan. Set aside.

In a small bowl, add 1/3 cup of milk and 2 tablespoons of lemon juice, and stir to combine. Let sit about 10 minutes. (The mixture will curdle into sour milk.)

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

In a large bowl, beat the butter with an electric mixer on medium speed for about 10 seconds, or until smooth.  Beat in the granulated sugar until well blended and light and fluffy, about 2 minutes. Beat in the eggs, one at a time, beating after each egg is added. Beat in the vanilla and lemon zest.

Alternate adding the flour mixture and the milk mixture to the butter mixture, beating on low after each addition, until the batter is just combined.

Pour the cake batter into the prepared pan.  Bake in preheated oven for 45 minutes (or until a toothpick inserted into the middle comes out clean).  Cool slightly, then remove the cake from the pan to finish cooling on a wire rack.

Once the cake has cooled, make the glaze. In a medium bowl, whisk together the confectioner’s sugar, 2 teaspoons of lemon juice, and 1 tablespoon of milk. (Whisk in more milk as needed until thick and spreadable.  Add more confectioner’s sugar if necessary.)

Spoon the glaze over the top of the cake, so it can drizzle down the sides.