Start by browning the butter for the sponge. Place butter in a saucepan and melt, stirring continuously. Once melted, the butter will foam up, then subside. Watch carefully as lightly browned specks form at the bottom of the pan. Remove from heat and let cool.
Preheat the oven to 340°F.
Line and lightly grease a bundt pan.
Mix together the milk and vinegar, then set aside for 10 minutes.
Once thickened, pour into a large mixing bowl and add the remaining wet ingredients, including the cooled brown butter.
Sift in the dry ingredients and gently mix until just combined.
Pour the batter into the bundt pan.
Bake for 35-40 minutes, or until the center is set and well risen.
When the cake has a few minutes left to bake, prepare the glaze by mixing the powdered sugar, milk, and cinnamon in a medium bowl until smooth.
Once the cake is done, flip it upside down onto a plate. Let it cool for 15 minutes before removing the pan.
Pour the glaze over the top of the cake, spreading it to cover completely.
Let the glaze set for about 20 minutes before serving.