Cream the softened butter and white sugar in a stand mixer or with electric beaters. Add milk, extracts, eggs, baking powder, flour, and salt, and beat until just combined. Set aside
Preheat the oven to 350 degrees.
Peel and slice the peaches, set the peels aside! Discard the pits.
Melt the other ⅓ cup of butter in a small saucepan over medium heat.
Once the butter is melted, add in the brown sugar and stir to combine. Turn the heat to medium low.
Once it is syrupy but not burning, add the peaches and stir to combine. Remove from heat and set aside.
Spray a bundt pan with cooking spray and pour in the peach mixture. Make sure it is evenly distributed, then slowly pour in the cake batter mixture. Make sure it is also evenly distributed and it should cover all of the peach mixture.
Bake for 45 minutes at 350 degrees.
Let cool for about 5 minutes, then put a plate over the bottom of the pan and gently flip it over. The cake should dislodge easily from the pan and is ready to eat.
Serve with additional sliced peaches, or peach or vanilla ice cream if desired.