Preheat the oven to 375°F (190°C). Bring a large saucepan of water to a boil.

Score the stem end of each peach and place them in the boiling water for about 1 minute or until the skins soften. Transfer to a bowl of cold water to cool, then peel, halve, and pit the peaches.

In a 9-inch cast-iron skillet, combine 1/3 cup sugar with 1 tablespoon butter. Cook over medium heat for 3 to 5 minutes until the sugar begins to melt. Arrange the peaches in the skillet cut-side up. Remove from heat.

In a medium bowl, mix flour, baking powder, baking soda, cinnamon, and salt. Set aside.

In a large bowl, beat the remaining sugar, butter, and oil until combined. Add the egg and beat until smooth, then add vanilla extract, almond extract, buttermilk, and the dry flour mixture. Mix until just incorporated.

Spoon the batter evenly over the peaches in the skillet. Bake uncovered at 375°F (190°C) for 20 to 25 minutes until a tester inserted in the center comes out clean.