Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease a 9x9 inch square baking pan.
Prepare the streusel by mixing 1.5 cups flour, 1/2 cup granulated sugar, 1/2 cup brown sugar, and cinnamon in a bowl. Pour in melted butter and stir until large crumbs form. Set aside.
Prepare the filling by beating the softened cream cheese, 1/4 cup sugar, one egg, and vanilla extract until smooth. Set aside.
In a medium bowl, whisk together 2 cups flour, baking soda, baking powder, salt, and pumpkin pie spice.
In a large bowl, whisk together the pumpkin puree, vegetable oil, two eggs, 1 cup sugar, and 1/2 cup brown sugar until well combined.
Gradually fold the dry ingredients into the wet ingredients until just combined, being careful not to overmix.
Spread approximately two-thirds of the pumpkin batter into the prepared baking pan.
Spread the cream cheese filling evenly over the batter.
Dollop the remaining pumpkin batter over the cream cheese layer and gently spread to cover.
Evenly distribute the streusel topping over the final layer of batter.
Bake for 50 to 55 minutes, or until a wooden skewer inserted into the center comes out clean.
Allow the cake to cool completely in the pan on a wire rack before slicing.