In a small saucepan, cook the butter over medium heat until brown and fragrant. When brown specks begin to form at the bottom of the pan, immediately transfer the butter to a small bowl. Let cool to room temperature.
Preheat the oven to 350ºF (180ºC). Line the bottom of an 8 x 4-inch baking pan with parchment paper. Grease and flour the insides.
In a medium-sized bowl, beat the brown butter, brown sugar, eggs, vanilla and buttermilk until smooth and creamy. Stir in the flour mixture in two additions. Mix just until combined.
Transfer the batter to prepared baking pan. Bake until the top is deep golden brown and a toothpick inserted into center comes out clean, about 38-43 minutes.
Let the bread cool in pan for 10 minutes, them turn it out onto a cooling rack to cool completely. Top the cooled cake with two coats of butterscotch glaze.