Prep the Oven and Pan: Preheat your oven to 325°F (165°C). Generously grease a 9x5-inch light-colored loaf pan with non-stick baking spray or butter, and line the bottom and long sides with a sling of parchment paper for easy removal.
Cream Butter and Sugar: In the bowl of a stand mixer fitted with the paddle attachment (or using a high-powered hand mixer), beat the softened butter on medium speed until smooth, about 1 minute. Gradually pour in the granulated sugar. Beat on medium-high speed for a full 4 to 5 minutes. The mixture must be pale, light, and visibly fluffy. Do not skip or shorten this step!
Incorporate the Eggs: Reduce the mixer speed to low. Add the room-temperature eggs one at a time. Allow each egg to fully blend into the batter before adding the next. Stop the mixer and scrape down the sides and bottom of the bowl with a rubber spatula halfway through to ensure even mixing.
Add Flavor: Mix in the pure vanilla extract.
Mix Dry Ingredients: In a separate medium bowl, thoroughly whisk together the sifted cake flour and kosher salt.
Combine Wet and Dry: With the mixer on the lowest possible speed, gradually add the dry ingredients to the butter mixture in three additions, alternating with the room-temperature whole milk (start and end with the flour). Mix just until the flour disappears. Do not overmix! Finish folding the batter gently by hand with a silicone spatula to ensure no dry pockets remain hidden at the bottom.
Bake: Pour the thick batter into your prepared loaf pan, smoothing the top into an even layer with your spatula. Bake in the preheated oven for 65 to 75 minutes. Check the cake at the 55-minute mark; if the top is browning too quickly, tent it loosely with aluminum foil. The cake is done when a long wooden skewer inserted all the way into the center comes out clean or with just a few moist crumbs attached.
Cooling: Allow the cake to cool in the pan on a wire rack for exactly 15 minutes. Then, use the parchment paper sling to carefully lift the cake out of the pan and transfer it directly to the wire rack to cool completely before slicing.