Set the oven to 350°F (175°C). Lightly grease an 8.5 x 4.5-inch loaf pan, then fit it with parchment paper so the baked cake can be removed cleanly.
Place the all-purpose flour, granulated sugar, baking powder, and salt in a large mixing bowl. Using a hand mixer or stand mixer fitted with the paddle attachment, mix until the dry ingredients are evenly distributed.
Add the softened unsalted butter to the dry mixture. Beat at medium speed only until the butter is completely worked into the ingredients and the mixture appears smooth and cohesive. Avoid excessive mixing at this stage.
In a separate 2-cup measuring vessel, whisk together the eggs, milk, vanilla extract, neutral oil, lemon zest, and lemon juice.
Keep the mixer operating at medium speed and gradually stream the liquid mixture into the butter and flour base. Continue mixing until the batter is evenly combined.
Should the batter remain slightly lumpy, increase the mixer speed for 10 to 15 seconds, stopping as soon as the texture becomes smooth.
Use a rubber spatula to fold the batter several times by hand, scraping along the bottom and sides of the bowl to eliminate any remaining pockets of dry flour.
Transfer the finished batter to the prepared loaf pan. Smooth the surface into an even layer with a spatula.
Bake for 1 hour to 1 hour 10 minutes. The loaf is ready when the top is puffed and golden brown, with a pronounced crack running through the center.
Remove the pan from the oven and leave the cake to cool at room temperature for approximately 45 minutes.
While the loaf cools, place the sifted confectioners’ sugar, lemon juice, and milk or heavy cream in a bowl. Whisk until completely smooth and thick enough to resemble the consistency of glue.
When the glaze is too fluid, incorporate a small amount of additional confectioners’ sugar. When it is overly thick, loosen it with very small additions of milk or cream until the proper texture is reached.
Once the loaf has cooled completely, lift it from the pan and position it on a serving plate or wire rack.
Pour the lemon icing over the surface. Guide it gently with a spatula, allowing some of the glaze to flow naturally down the sides.
Let the icing firm slightly before cutting the loaf into slices.