Preheat oven to 350 degrees. Measure and cut parchment paper to fit your 8-inch cake pans. Grease cake pans and then place parchment paper circles on top. Set aside.
Add 1 ½ cups of sugar and softened butter to a bowl fitted for a stand mixer. Whip until light and fluffy, about 4 minutes. Scrape the sides of the bowl and mix 10 seconds more.
Add eggs one at a time, mixing well after each one. Add vanilla and mix together until combined.
In a separate bowl, whisk flour, salt, and baking powder until combined. Add half of the mixture to the butter mixture. Mix until combined. Add milk and mix until combined. Finish with the rest of the flour mixture. Mix just until combined. Do not overmix!
Divide batter between the two prepared cake pans. Place in preheated oven to bake until cake is cooked through, about 25 minutes. Remove when ready and let cool for 10 minutes in their pans before removing and cooling completely on racks.