1. In a small saucepan, melt the butter over medium-low heat and continue to cook, swirling occasionally, until butter turns golden brown, Skim foam from top, and remove from heat. Pour into a bowl to stop the cooking, leaving any burned sediment behind.
2. Combine browned butter, sugar, and buttermilk in a large saucepan. Heat over medium heat and whisk together until sugar dissolves. When butter mixture starts to boil, carefully whisk in the baking soda and vanilla. The mixture will bubble up, so make sure you use a large saucepan. Serve with waffles, pancakes, or French toast.
Note-syrup will keep in the refrigerator for up to 2 weeks. Reheat before serving.