Preheat the oven to 375 degrees F. Add the butter to a 10-12 inch oven-safe skillet set over medium heat. Allow the butter to brown lightly until it smells toasted, about 2-3 minutes. Stir often. Remove from the heat and carefully pour the butter into a large mixing bowl. Line the skillet with parchment paper, then rub with additional butter, making sure every inch of the parchment-lined skillet has been buttered. Set the skillet aside.

To the mixing bowl with the browned butter, add the yogurt, eggs, ¾ cup sugar, the vanilla, and milk, beating until combined. Add the flour, baking powder, ½ teaspoon cinnamon, and the salt. Mix until just combined.

In a small bowl, mix the remaining ¾ cup sugar and 1 tablespoon cinnamon.

Sprinkle the bottom of the buttered skillet with 3 tablespoons of cinnamon sugar. Arrange the peach slices in a single layer over the sugar, then sprinkle the peaches with 2 tablespoons cinnamon sugar. Pour the cake batter over the peaches. Sprinkle the top of the cake with 2 tablespoons cinnamon sugar, then arrange the remaining peach slices on top. Sprinkle with the remaining cinnamon sugar.

Place the skillet on a baking sheet. Bake 40-45 minutes, until golden brown and a knife inserted into the center of the cake comes out clean. Let the cake cool in the skillet for 5 minutes. Run a knife around the edge to loosen. Carefully invert the cake onto a serving plate. Let cool slightly.

In a large bowl, using an electric mixer, beat the cream and bourbon on medium-high speed until soft peaks form, 3-4 minutes. Cut the cake into wedges. Serve warm, topped with whipped cream.