To make your amazing Peach Cobbler Cheesecake, follow these comprehensive steps:

1. Preheat the Oven: Set your oven to 325°F (163°C) and grease a 9-inch springform pan.
2. Make the Cheesecake Batter: In a large bowl, beat the softened cream cheese with an electric mixer until creamy. Gradually add the sugar and mix until fully combined.
3. Add Sour Cream: Mix in the sour cream until smooth.
4. Incorporate Eggs and Extracts: Add the eggs one at a time, mixing well after each addition. Stir in the vanilla and almond extracts.
5. Fold in Peaches: Gently fold in the sliced peaches with a spatula until evenly distributed.
6. Pour into Pan: Pour the cheesecake mixture into the prepared springform pan and smooth the top.
7. Prepare the Cobbler Topping: In a separate bowl, combine the flour, sugar, baking powder, and salt. Pour in the melted butter and milk, mixing until just combined. Do not overmix.
8. Top the Cheesecake: Spoon dollops of the cobbler mixture over the cheesecake batter, spreading it gently.
9. Bake: Place the springform pan in the preheated oven and bake for 50-60 minutes, or until the center is mostly set but slightly jiggly.
10. Cool: Turn off the oven, crack the oven door, and let the cheesecake cool inside for about 1 hour. Then, cool at room temperature and refrigerate for at least 2-3 hours, preferably overnight.
11. Serve: Before serving, run a knife around the edge of the cheesecake to loosen it from the pan. Carefully remove the sides of the springform pan. Optionally, top with whipped cream and fresh peach slices.