Preheat an oven to 350 F.
Make the crust. In a mixing bowl, beat the butter and sugar together with a hand mixer until light and fluffy, about 4-5 minutes. Mix in the vanilla, salt, and flour until crumbly. Press the crust in an even layer into the prepared baking pan and chill for 1 hour. Bake for 20 minutes, until lightly browned, and cool slightly.
Prepare the apples. Melt the butter in a nonstick skillet over medium-high heat. When the butter is melted and foamy, add the diced apples and cook for 2-3 minutes, until slightly browned. Sprinkle in the vanilla, salt, and sugar and stir well. Cook for 3-4 minutes, until the apples get syrupy, then sprinkle in the flour. Stir well and cook for another 3-4 minutes until very thick. Remove from the heat and cool to room temperature.
Make the crumble. Mix the flour, brown sugar, oats, pecans, pecans and cinnamon together in a small mixing bowl with a fork. Mix in the butter with your fingers until clumps form. Refrigerate until ready to use.
Make the cheesecake filling. In a mixing bowl, beat the cream cheese and sugar until smooth. Mix in the sour cream and the eggs and yolk, one at a time. Mix in the vanilla and beat until very smooth.
Adjust oven temperature to 325 F.
Assemble the bars. Pour the cheesecake filling into the baked and cooled crust and spread into an even layer. Top evenly with the sautéed apples and sprinkle the crumble evenly over the top.
Bake. Bake for 60-70 minutes, until the center slightly jiggles but is set. Remove from the oven and cool to room temperature, then chill for at least 4 hours before serving the apple cheesecake bars.