Preheat oven to 350°F and spray a 10-inch springform pan with nonstick spray. For the crust, whisk together flour, graham cracker crumbs, baking soda, salt, cinnamon, and nutmeg in a medium bowl. Combine melted butter and sugars in a medium bowl. Add flour mixture and fold in until incorporated. Use a piece of parchment paper lightly coated with nonstick spray to press dough evenly into bottom of prepared pan. Bake crust for 18 minutes, until golden and set. Transfer to a wire rack to cool completely.
Reduce oven temperature to 325°F. For the filling, beat cream cheese and sugar in a large mixer bowl at medium speed until smooth and creamy, about 3 minutes. Scrape down bowl with a spatula as needed. Add yogurt, vanilla, cinnamon, and salt, and beat until combined, about 1 minute. Reduce speed to low, add the eggs one at a time, and mix until just incorporated. Pour filling over cooled crust; smooth top with an offset spatula.
Bake at 325°F for 55 minutes, until the sides of the cheesecake are slightly puffed. Turn oven off, prop open oven door with a wooden spoon, and let cheesecake sit in the oven for 1 hour. Remove cheesecake from oven and cool to room temperature on a wire rack for 2 hours. Run a knife around the top edge of the cheesecake to loosen it from pan; cover and chill overnight.
For the salted caramel sauce, combine brown sugar, butter, and heavy cream in a heavy saucepan. Bring to a boil over medium heat, stirring constantly until butter has melted completely. Reduce heat to low and simmer 5 minutes, stirring occasionally. Remove from heat and stir in vanilla and salt until smooth. Pour sauce into a glass bowl to cool to room temperature.
For the apple topping, combine butter and brown sugar in a large skillet and melt over medium-high heat. Add apples, cinnamon, and nutmeg, and cook until lightly caramelized and soft, about 5 minutes. Transfer apples to a bowl and cool slightly.
When ready to serve, remove side of pan and transfer cheesecake to a plate. Top cheesecake with warm apple topping, drizzle with caramel sauce, and sprinkle with pecans.