Preheat your oven to 350°F (175°C). Line a 9-inch cake pan (avoid using a springform pan) with parchment paper and generously butter the paper. Arrange the peach wedges over the parchment, starting at the center and spiraling outward. Sprinkle 1/4 teaspoon of ground cinnamon over the peaches.
In a small saucepan, combine 1/4 cup water and 1/2 cup sugar. Stir to combine. Heat the mixture over medium-high heat without stirring further until it turns a light brown caramel color, which should take about 10-15 minutes. Remove from heat, quickly add 1 tablespoon bourbon (the caramel will bubble), then immediately pour the caramel evenly over the arranged peaches. I always keep a close eye on caramel, as it can change color quickly!
In a large bowl, beat together 8 tablespoons unsalted butter and 3/4 cup sugar until the mixture is light and fluffy, about 3 minutes. Add the eggs one at a time, beating well after each addition. Beat in the vanilla extract and 2 tablespoons bourbon. In a separate bowl, whisk together 1 cup all-purpose flour, 1/4 cup almond flour, 1 teaspoon baking powder, and the remaining 1/4 teaspoon ground cinnamon. Gradually beat the dry ingredients into the wet mixture until combined and smooth.
Carefully pour the cake batter over the peaches and caramel in the prepared pan. Use a spatula to gently smooth the surface so that the batter covers the peaches evenly. Bake in the preheated oven for 30-35 minutes, or until a toothpick or knife inserted into the center comes out clean.
Once the cake is finished baking, let it cool in the pan for 15-30 minutes. After cooling, run a knife around the edge of the pan, then carefully invert the cake onto a serving plate, removing the parchment paper to reveal the caramelized peaches on top. For a finishing touch, I like to serve it slightly warm with a scoop of vanilla ice cream.