Preheat your oven to 350F and grease an 8” round cake pan with non-stick cooking spray.
In a large bowl, cream the butter and sugars together until slightly pale and fluffy. Add the egg, beating well, then stir in the vanilla and yogurt. In a separate bowl, sift the flour, baking powder, baking soda, and salt together. Add the dry mixture to the wet and stir just to combine.
Pour the batter into the prepared cake pan, top with the peaches and pecans. Bake for 30 to 40 minutes or until a toothpick inserted into the centre of the cake comes out clean. Allow the cake to cool in the pan and prepare the bourbon caramel.
For the bourbon caramel, pour the water into a medium saucepan over medium-high heat and top with the sugar. Do not stir this mixture at all prior to adding the cream as this will cause crystals to form and prevent your caramel from being silky smooth.
Cook the water and sugar mixture until it becomes a deep golden colour, approximately 10 to 13 minutes. Remove the caramel from the heat and carefully whisk in the cream followed by the bourbon. Return the caramel to the heat and cook, stirring frequently over medium-low, until the caramel has thickened quite a bit. This should take approximately 10 minutes. If there are lumps in your caramel after adding the cream, that's ok. Just keep whisking over the heat and they should dissolve.
Once thickened, remove the caramel from the heat and whisk in the butter, vanilla, and salt. Set aside and allow to cool slightly and serve over the cake.