Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan with cooking spray or line it with parchment paper.
In a large mixing bowl, whisk together the pumpkin puree, egg, brown sugar, oil, sour cream, and vanilla extract until smooth and well combined.
In a separate bowl, whisk together the pumpkin pie spice, flour, baking powder, baking soda, and salt.
Gradually fold the dry ingredients into the wet mixture, stirring gently until just combined. Do not overmix.
In another medium bowl, whisk together the egg, softened cream cheese, granulated sugar, and flour until smooth and creamy.
Pour two-thirds of the pumpkin bread batter into the prepared loaf pan, spreading it evenly with a spatula.
Gently pour the cream cheese filling over the batter, spreading it carefully to reach the edges.
Top with the remaining pumpkin batter, spreading it as evenly as possible to cover the cream cheese layer.
Bake for 45–50 minutes, or until a toothpick inserted into the center comes out mostly clean with only a few moist crumbs.
Let the bread cool in the pan for 15 minutes, then transfer it to a wire rack to cool completely before slicing.