Preheat your oven to 350°F. Place a rack in the center of the oven. Line a 4x6-inch mini loaf pan with parchment paper, leaving an overhang on the long sides to lift the cake out. Lightly grease the parchment and exposed pan with nonstick spray or butter.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until well combined.
In a separate large mixing bowl or the bowl of a stand mixer with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 3-5 minutes. Scrape down the sides of the bowl as needed.
Add the egg and beat on medium speed until fully incorporated and slightly thickened, about 30 seconds to 1 minute. Beat in the vanilla.
With the mixer on low speed, add the dry ingredients in 2 additions, alternating with the milk in 1-2 additions, beginning and ending with the dry ingredients. Mix just until each addition is incorporated and no streaks of flour remain. Do not overmix.
Scrape the batter into the prepared pan and smooth the top with a spatula.
Bake until the top is golden, the sides are just beginning to pull away from the pan, and a toothpick inserted in the center comes out clean or with a few moist crumbs attached, 40-45 minutes.
Let the cake cool in the pan on a wire rack for 10 minutes.
Use the parchment overhang to lift the loaf out of the pan, then transfer it directly to the rack to cool completely, about 30-45 minutes.
Serve right away or store in an airtight container.