Prepare the Peach Cobbler Topping:
In a skillet, melt the butter over medium heat.
Add sliced peaches, brown sugar, cinnamon, nutmeg, and vanilla. Cook until the peaches soften and release their juices (about 5–7 minutes).
Stir in the cornstarch slurry and cook until the mixture thickens.
Let cool completely.
Assemble the Cheesecake:
Top the chilled cheesecake with the peach cobbler mixture, spreading it evenly.
Serve & Enjoy: