1. Center a rack in the oven and preheat the oven to 325 degrees F. Butter a 9x5-inch loaf pan or an 8-1/2 x 4-1/2-inch loaf pan. Put the pan on an insulated baking sheet or on two regular baking sheets stacked one on top of the other.
2. Whisk together the flour, baking powder, and salt.
3. Working with a stand mixer, preferably fitted with a paddle attachment, or with a hand mixer in a large bowl, beat the butter and sugar on high speed until pale and fluffy, a full 5 minutes. Scrape down the bowl and beater and reduce the mixer speed to medium. Add the eggs one at a time, beating for 1 to 2 minutes after each egg goes in. As you're working, scrape down the bowl and beater often. Mix in the vanilla extract. Reduce the mixer speed to low and add the flour, mixing only until it is incorporated - don't overmix. In fact, you might want to fold in the last of the flour, or even all of it, by hand with a rubber spatula. Scrape the batter into the buttered pan and smooth the top.
4. Put the cake into the oven to bake, and check on it after about 45 minutes. If it's browning too quickly, cover it loosely with a foil tent. If you're using a 9x5 pan, you'll need to bake the cake for 70 to 75 minutes; the smaller pan needs about 90 minutes. The cake is properly baked when a thin knife inserted deep into the center comes out clean.
5. Remove the cake from the oven, transfer the pan to a rack and let rest for 30 minutes.
6. Run a blunt knife between the cake and the sides of the pan and turn the cake out, then turn it right side up on the rack and cool to room temperature.
Wrapped well, the cake will keep for 5 to 7 days at room temperature (stale cake is great toasted) or up to 2 months in the freezer.