Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan and line the bottom with parchment paper.

1. For the topping: In a medium skillet, melt the butter over medium heat. Add the brown sugar and cook for 3-4 minutes, stirring occasionally, until the mixture begins to bubble and thicken. Stir in the bourbon, vanilla extract, and pinch of salt. Let it simmer for another minute until smooth and glossy.
2. Pour the bourbon caramel syrup into the prepared cake pan, spreading it evenly. Arrange the peach slices in a circular pattern over the syrup.
3. For the cake: In a medium bowl, whisk together the flour, baking powder, and salt. In a separate bowl, beat the butter and sugar together until light and fluffy. Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
4. Gradually add the dry ingredients to the wet ingredients, alternating with the milk, until just combined. Be careful not to overmix.
5. Pour the batter over the caramelized peaches in the cake pan, smoothing the top with a spatula. Bake for 40-45 minutes or until a toothpick inserted into the center comes out clean and the top is golden brown.
6. Let the cake cool in the pan for 10 minutes. Run a knife around the edges, then invert the cake onto a serving plate. Remove the parchment paper and let the cake cool slightly before serving.