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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.
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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.
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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.
Make Ahead
The cake can be kept at room temperature, covered, for up to 3 days.