Preheat oven to 350°F (175°C). Line a 9-inch cake pan (not a springform pan) with parchment paper and butter the paper.
Arrange peach wedges over the parchment, starting from the center and working your way out. Sprinkle ¼ teaspoon cinnamon over the peaches.
In a medium saucepan, combine ¼ cup water and ½ cup sugar. Stir gently to combine, then heat over medium-high heat without stirring until the mixture turns a light brown caramel color (about 10-15 minutes). Remove from heat and quickly add 1 tablespoon bourbon. Pour evenly over the peaches.
In a mixing bowl, beat together the butter and ¾ cup sugar until light and fluffy (about 3 minutes). Beat in eggs one at a time, then mix in vanilla extract and the remaining 2 tablespoons bourbon.
In a separate bowl, whisk together the all-purpose flour, almond flour, baking powder, and remaining ¼ teaspoon cinnamon. Slowly beat the dry ingredients into the wet ingredients until combined.
Pour the batter over the peaches and smooth the surface.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool for 15-30 minutes before turning it out onto a serving plate. Carefully remove the parchment paper and serve.