Preheat the oven to 190°C /Fan 170°C/Gas 5 and grease a 28cm bundt tin. Heat the butter in a pan set over a gentle heat until it turns nut brown. Remove from the heat and cool for 10 minutes.
In a stand mixer, beat together the brown butter, sugar and vanilla. Add the eggs one at a time, beating after each addition, then beat in the buttermilk. Fold in the flour and salt and mix until smooth. Pour the batter into the tin and bake for 1 hour.
Just before the cake is ready, make the bourbon butter glaze. Pop the butter into a pan over a gentle heat and cook until it turns nut brown. Add the sugar, keeping the pan over the heat until the sugar has dissolved. Pour in the bourbon and stir.
Tip the cake onto a plate and, while it is still warm, spoon the glaze over the top. Once cool, fill the centre with whipped cream and serve.