Set the oven rack to the center position. Preheat to 350ºF (176ºC). Lightly grease a 9×5-inch loaf pan with butter and coat it with flour, tapping out the excess.

In a medium bowl, whisk together the flour, baking powder, and salt.

In a stand mixer fitted with a whisk attachment or hand mixer, beat the softened butter on medium speed for 1 minute. Slowly add the sugar while mixing for 30 seconds. Continue mixing until light and fluffy, scraping down the bowl halfway through, about 3 minutes.

Add the eggs one at a time over medium speed, mixing until incorporated, about 20-second intervals while scraping down the side of the bowl after each addition.

Mix in the sour cream and vanilla over medium speed, about 15 seconds. Scrape down the sides of the bowl.

Add the flour mixture and mix over low speed until just combined, about 10 seconds. Use a spatula to mix in any remaining flour pockets. Do not overmix!

Pour the batter into the greased pan and smooth the top with a spatula. Bake until the surface is golden brown and a toothpick inserted comes out mostly clean, or the internal temperature reaches 200 to 205ºF (93 to 96ºC), about 45 to 50 minutes.

Cool the bread in a pan for 10 minutes. Carefully run a knife around the sides of the pan. Use the parchment paper sling to remove the pound cake and transfer it to a wire cooling rack. Cool completely before slicing.