In a medium bowl, beat the softened cream cheese, sugar, egg, and flour until smooth. Set aside.
In a large bowl, whisk together the pumpkin purée, granulated sugar, brown sugar, eggs, vegetable oil, and vanilla extract until well combined.
In a separate bowl, stir together the flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Preheat oven to 325°F. Grease two 8x4-inch loaf pans.
Pour half of the pumpkin batter into the prepared pan and spread evenly. Carefully spread the cream cheese filling over the batter. Pour the remaining pumpkin batter over the cream cheese layer, smoothing the top.
Bake for 60-70 minutes, or until a toothpick inserted into the center comes out clean. Cover during the last 15 minutes of baking to prevent overbrowning.
Allow the bread to cool in the pan for 15 minutes, then transfer it to a wire rack to cool completely before slicing.