Brown the Butter: In a saucepan, melt the unsalted butter over medium heat. Allow the butter to simmer, stirring occasionally, until it turns a golden brown color and emits a nutty aroma. Remove from heat and let it cool slightly.

Preheat and Prepare: Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan, ensuring it’s well-coated to prevent sticking.

Mix Dry Ingredients: In a mixing bowl, whisk together the flour, baking powder, baking soda, and salt until well combined.

Combine Wet Ingredients: In another bowl, whisk together the granulated sugar, eggs, and vanilla extract until smooth. Gradually add the cooled brown butter, whisking continuously until fully incorporated.

Incorporate Dry Ingredients: Alternately add the dry ingredients and buttermilk to the wet mixture, beginning and ending with the dry ingredients. Mix until just combined, being careful not to overmix.

Bake the Cake: Pour the batter into the prepared cake pan and smooth the top with a spatula. Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.

Cool and Serve: Allow the cake to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely. Once cooled, slice and serve the cake, savoring each delectable bite.