Preheat oven to 350 degrees and spray 9 x 13 baking dish with nonstick baking spray.
In medium bowl combine 6 tablespoons butter, 1/3 cup flour, brown sugar, rolled oats and 1 teaspoon cinnamon. Using pastry knife cut in butter until crumbly. Set aside.
In medium bowl whisk together 1 3/4 cups flour, baking soda, baking powder, salt and pumpkin pie spice.
In stand mixer with paddle attachment cream 1/2 cup butter with 1 1/2 cups sugar. Turn mixer to stir. Add 3 eggs; 1 at a time mixing after each just until blended. Add pumpkin puree and applesauce and mix just until incorporated. Add flour mixture (not crumb mixture made in step 1) in three parts mixing just until incorporated.
In medium bowl with hand mixer beat cream cheese and 1/3 cup sugar until smooth and creamy. Add 1 egg and vanilla and mix just until incorporated.
Spread half of the pumpkin cake mixture in the pan. Carefully spread the cream cheese mixture over the cake mixture. Now add the rest of the cake mixture spreading carefully with a spatula. Some may bleed through. Do not overwork or it the cream cheese mixture will be absorbed by the pumpkin mixture.
Sprinkle with the crumb topping and bake for 50 minutes or until set. Allow to cool 20 minutes before cutting.
Video
Notes
Grease and flour your baking dish well. I like to use Baker's Joy which is a nonstick baking spray with flour.
Always preheat your oven and load the cake in the center of the oven.
For best results use real unsalted butter.
Do not overwork the cream cheese mixture or it will get absorbed into your cake.
Bake the cake until set. Test with a toothpick for doneness but please keep in mind that a little bit of cream cheese is going to end up on your toothpick and the cake may still be done.
Refrigerate leftovers as the cake has cream cheese in it