Preheat oven to 350. Line a 13×9 pan with foil or parchment paper and then lightly spray with cooking spray. You could also just spray the baking pan. Lining it with foil makes the bars easier to take out of the pan and cut into squares.
Make the crumble. Mix flour, brown sugar, and sugar in a bowl. Cut in butter with pastry blender or clean hands, until mixture resembles coarse crumbs. Stir in oats and pecans.
Reserve a heaping 1 cup of this mixture. Press the remaining into the bottom of the pan. Bake for 15 minutes.
While the crust is cooking prepare the pumpkin cheesecake. Add the cream cheese, pumpkin, eggs, sugar, and pumpkin pie spice in the bowl of a mixer, or with a hand blender, and beat on medium speed until well blended. Pour over the cooked crust and sprinkle with the reserved crumb mixture. Press down lightly.
Bake for 23-25 minutes. The middle may look "jiggly" still but the outside edges will look done. That's how you want it.
Let cool for 1 hour in the pan. Cover the baking dish with plastic wrap and let it refrigerate for 3 hours. Once done, lift bars out of the pan and cut into squares. Store leftovers in the fridge.