Preheat your oven to 350°F and lightly grease a 9x13 baking dish. Pour the sliced peaches with their syrup into the dish. Add brown sugar, cinnamon, nutmeg, vanilla extract, lemon juice, and cornstarch, then stir until the peaches are evenly coated.
In a separate mixing bowl, beat the softened cream cheese, granulated sugar, egg, and vanilla extract until smooth and creamy. The mixture should be soft enough to spoon over the peaches but thick enough to hold some shape.
Drop spoonfuls of the cheesecake mixture over the peach filling. Gently swirl the cream cheese into the peaches, but do not fully mix it in. Leaving pockets of cheesecake gives the dump cake its rich, creamy texture.
Sprinkle the dry yellow cake mix evenly over the top of the peach and cheesecake layers. Do not stir the cake mix into the filling. Spread it out gently so the surface is covered.
Drizzle the melted butter evenly over the cake mix, trying to cover as much of the dry mix as possible. Sprinkle the remaining cinnamon over the top. Add chopped pecans if using.
Bake for 45 to 55 minutes, or until the top is golden brown and the peach filling is bubbling around the edges. If you see dry cake mix spots near the end, drizzle a little extra melted butter over those areas and continue baking.
Remove the dump cake from the oven and let it rest for 15 to 20 minutes before serving. This helps the peach filling thicken and gives the cheesecake layer time to set.
Serve warm with vanilla ice cream, whipped cream, or a drizzle of caramel sauce.