Preheat the oven to 350 degrees F and mist a 9x5-inch loaf pan with non-stick spray. Lay a sheet of parchment in the bottom and up the sides of the pan, and set aside.
In a large bowl, beat the butter on medium-high speed until shiny (about 15 seconds).
With the mixer still running, slowly add the sugar in a steady stream.
After about 30 seconds, when all the sugar has been added, beat the mixture on medium-high for 5 full minutes, until very fluffy and pale white.
Place the eggs and yolks in a small bowl and beat with a fork.
While the mixer is running, pour the eggs down the side of the bowl in a thin stream.
Add the vanilla and salt.
Turn off the mixer and place a sieve over the bowl.
Sift in 1/2 cup cake flour, then fold carefully until just combined. Repeat twice, until all the flour has been incorporated.
Transfer the mixture to the prepared loaf pan, and bake for 60-70 minutes, or until a tester inserted in the center of the cake comes out clean or with a few moist crumbs.
Cool for 20 minutes before removing from the pan.
Slice and serve with Gingered Brown Butter Peaches and whipped cream.