Preheat oven to 325 degrees. Liberally grease and flour a 9 or 10 cup bundt pan.
Mix together the flour, baking soda, and salt. Set aside.
Add the butter, brown sugar, and sugar to a large mixing bowl. Beat on medium speed until light and fluffy.
Mix in the eggs, one at time, beating well after each egg.
Add half of the flour to the mixture and stir by hand to combine, followed by half of the buttermilk mixture and the vanilla. Repeat with the remaining flour and buttermilk, mixing until the batter is just combined.
Pour mixture into prepared pan and bake for 70-80 minutes or until the cake springs back when you touch the top and the edges begin to pull away from the side of the pan.
Let cool in the pan for 10 minutes before turning out onto a cake plate to finish cooling.
For the glaze
When the cake has cooled completely, add the butter to a small sauce pan over medium heat.
When butter has melted completely, begin whisking it. It will foam up as it cooks. Continue whisking and keep a close on the butter as it begins to brown.
Remove the butter from the heat when the liquid is golden brown.
Whisk in the powdered sugar and milk to form a smooth glaze.
Immediately pour glaze over the cooled cake. Glaze will set within minutes.
I'm getting a few comments from readers that this is turning out too dry and the bake time is off. Please start checking the cake at 1 hour with a tester. It should come out mostly clean with just a few moist crumbs.