Preheat oven to 350 degrees. Line the bottom of an 8 1/2-by-4 1/2-by-2 1/2-inch loaf pan with parchment paper.
In a medium bowl, mix together milk, eggs, and vanilla; set aside.
Place flour, sugar, baking powder, and salt in the bowl of an electric mixer fitted with the paddle attachment. Mix on low speed until well blended. Add butter and half of the milk mixture; continue mixing until moistened. Increase mixer speed to medium and beat for 1 minute.
Scrape down sides of bowl. Add half of the remaining milk mixture. Beat on medium speed for 30 seconds. Scrape down sides of bowl and add remaining milk mixture. Beat again on medium speed for 30 seconds.
Pour batter into prepared loaf pan. Bake until a toothpick inserted into the center of the cake comes out clean, about 1 hour.
While cake is still warm, invert onto a wire rack. Completely wrap in plastic wrap to keep cake moist.