Pound for pound, this cake is hard to beat!
Adjust oven rack to middle position and heat oven to 325 degrees. Spray inside bottom and sides of 8½-by-4½-inch metal loaf pan with vegetable oil spray with flour.
In large bowl, whisk together flour, baking powder, and salt. In liquid measuring cup, melt butter.
Add sugar, eggs, and vanilla to food processor and lock lid into place. Turn on processor and process until well combined, about 10 seconds.
With processor running, slowly pour hot melted butter through feed tube until combined, about 30 seconds. Stop processor.
Remove lid and carefully remove processor blade (ask an adult for help). Pour butter mixture into bowl with flour mixture, making sure to scrape all butter mixture into bowl using rubber spatula.
Use rubber spatula to gently stir batter until just combined and no dry flour is visible. Do not overmix. Scrape batter into greased loaf pan.
Place loaf pan in oven. Bake until cake is deep golden brown and toothpick inserted in center comes out with few crumbs attached, 55 minutes to 1 hour.
Use oven mitts to remove loaf pan from oven (ask an adult for help). Place loaf pan on cooling rack and let cake cool in pan for 15 minutes.
Carefully run butter knife around edges of cake to loosen from loaf pan (ask an adult for help—pan will be hot). Use oven mitts to carefully turn loaf pan on its side and remove cake from pan. Let cake cool completely on cooling rack, about 2 hours. Transfer cake to cutting board, cut, and serve.