Preheat your oven to 325 degrees F. Spray two 8-inch round cake pans with non-stick spray and then line with parchment. Spray again. Set aside.
In a medium sized mixing bowl, whisk together the cake flour, baking powder and salt. Set aside.
In the bowl of an electric mixer, fitted with the paddle attachment, cream the brown butter and the sugars for about 3 minutes on medium-high speed.
Scrape down the sides of the bowl and begin to add the eggs on medium speed, scraping down the sides and bottom of the bowl between addition, continue beating on medium-high speed until the texture is smooth and the volume is nearly doubled, about 3 to 5 minutes.
Add the vanilla bean paste or extract and beat until incorporated.
With the mixer on low speed, add 1/3 of the flour mixture, followed by 1/2 of the buttermilk. Repeat the additions, 1/3 flour mixture, second half of the buttermilk and the final 1/3 flour mixture. Only mix until the flour mixture is incorporated, about 30 seconds. Scrape down the sides and bottom of the bowl and mix again for another 20 to 30 seconds on low.
Divide the cake batter into each of the two 8-inch cake pans and bake for about 30 minutes, or until a toothpick inserted into the center of the cake comes out with a few moist crumbs on it. Let cool in the pans for about 15 minutes and then invert onto a wire rack to cool completely. (Tip: spray your wire cooling racks with nonstick spray).