Preheat the oven to 325°. Butter a 10-by-5-inch loaf pan. Line the bottom with a strip of parchment paper that extends 2 inches past the short ends of the pan.
In a bowl, using an electric mixer, beat the butter with the sugar, vanilla and salt at medium speed until fluffy, 3 minutes. Add the eggs, 2 at a time, beating between additions. Beat in the milk. Sift the flour over the batter and whisk it in until smooth. Scrape the batter into the prepared pan and smooth the surface.
Bake the cake for 1 1/2 hours, until it is cracked down the center, golden on top, and a toothpick inserted into the center comes out clean. Let the cake cool in the pan on a wire rack for 10 minutes, then unmold the cake and let cool completely.
The cake can be kept at room temperature, covered, for up to 3 days.