Preheat the oven to 350 degrees F (175 degrees C). Grease and flour two 9-inch round cake pans, or line with parchment paper.
Combine brown sugar and butter for cake in a bowl; cream with an electric mixer on medium speed until fluffy. Add vanilla extract, then add eggs, one at a time, beating on low speed just until they are mixed in.
Sift flour, baking soda, baking powder, and salt together in a separate bowl. Add flour mixture in 2 batches, alternating with buttermilk, beating batter on low speed until well mixed, scraping down the bowl by hand as needed. Pour batter evenly into the prepared pans.
Bake in the preheated oven until a toothpick inserted into the center of each layer comes out clean, 25 to 30 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Invert carefully onto a serving plate or cooling rack. Let cool, about 30 minutes.
While cake cools, combine brown sugar, 1/4 cup butter, milk, and flour for icing in a small saucepan over medium heat; bring to a boil. Continue to boil, stirring frequently to prevent burning, for 1 minute. Remove from heat and stir in 2 tablespoons butter and vanilla extract. Cool the mixture, stirring occasionally, until it is still warm (but not hot) and has thickened enough to spread.
Spread icing over the cake, moving fairly quickly because it will set as it cools. It will be a thin coating, not a thick layer. Let set completely before cutting into the cake.
Nutritional Facts
Per 12 servings
Calories: 467
Carbohydrate: 81g
Fat: 15g
Fiber: 1g
Protein: 4g
Sugar: 64g
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