Preheat oven to 350. Prepare your 10.5 x 15.5 inch pan (or your closest equivalent) with non-stick foil or baking spray and set aside.
Mix the brown sugars, white sugar, baking soda, baking powder, and flour. Add the melted butter and mix until everything is moistened. Pour 3/4 of the crumb mixture into the prepared pan and press down firmly. Mix the oats and cinnamon into the remaining crumb mixture and set aside.
Place the sour cream, softened cream cheese, and sugar into your mixer, and mix until smooth. Add the vanilla and flour and mix until combined. Add the eggs and mix until just incorporated, finishing the mixing with a rubber scraper. DO NOT OVERMIX!!
Pour filling over crust and carefully smooth out to within 1/4 inch of the edge of the crust. Place dollops of strawberry pie filling over the filling mixture at evenly spaced intervals. Carefully swirl it a bit and distribute the berries over the crust and filling.
Sprinkle remaining crumb mixture on top, and bake at 350 for 25-30 minutes until the topping is a light golden brown. Remove from oven and let cool on counter for 10 minutes, and then chill for several hours.