Adjust the oven rack to the middle position and heat the oven to 325 Fahrenheit. Grease a 9” by 5” loaf pan. Line it with parchement paper and grease it.
Beat the butter and sugar in the bowl of a standing mixer at medium-high speed until light, fluffy and almost white. This takes about 4-5 minutes, stopping the mixer once or twice to scrape down the sides of the bowl.
In a different bowl, stir together the eggs, vanilla and milk. With the mixer running at medium speed add egg mixture to the butter and sugar in a very slow, thin stream. Finally beat in the salt.
Place 1/2 cup of pastry flour in a sieve and sift it over the batter. Fold gently with a rubber spatula, scraping up from the bottom of the bowl, until the flour is incorporated. Repeat twice more, adding flour in 1/2 cup increments.
Pour the batter into the prepared pan, smoothing the top with a spatula.
Bake in a preheated oven of 325 Fahrenheit until a toothpick comes out clean, about 60-70 minutes. The cake should be a nice golden brown.
Let the cake rest in the pan on a cooling rack for 5 minutes before removing it from the pan. After you remove it from the pan, let it cool to room temperature.