Place butter in a medium-sized pan and cook over medium heat until butter is melted. Increase heat to just above medium and cook, stirring frequently until you see golden brown specks.
Remove from heat and pour into a heatproof bowl. Allow butter to cool completely (it should still be liquid, but should no longer be warm to the touch) before proceeding.
Measure pecans before chopping. To get my pecans very fine, I toss them in the food processor and pulse until they are fine. Do not pulse too far, or you’ll turn them into nut butter!
Whisk together buttermilk, eggs, and vanilla, then slowly drizzle into the flour mixture. Pause halfway through and at the end to scrape the sides and bottom of the bowl.
Evenly divide batter into prepared baking sheets and bake in center rack of 350F oven for 30 minutes or until a toothpick inserted in the center comes out clean.
Allow cakes to cool in their pans for 15 minutes before running a knife around the edge of the cake to loosen it from the pan then carefully invert onto a cooling rack.
Make icing by combing butter, cream cheese, brown sugar, vanilla extract, and salt in a large mixing bowl and use an electric mixer to beat until smooth.
Level cakes if needed and decorate with frosting. I did a smooth, light covering for the sides of the cake with thicker frosting in between layers and on top.