Preheat the oven to 350°F (180°C) and butter and line with parchment a 9 x 5-inch (23 x 12 ½ cm) loaf pan. Set aside.
To Make the Cream Cheese Filling
In a small bowl, whisk together the egg, cream cheese, sugar, flour and vanilla extract until smooth. Set aside.
To Make the Pumpkin Bread
In a medium bowl, whisk together the eggs, pumpkin puree, brown sugar, oil, milk and vanilla extract until smooth.
In a separate medium bowl, combine the flour, pie spice, salt and baking soda.
Combine the wet and dry ingredients together until just combined.
Spread half of the batter into the prepared pan, then layer in the cream cheese filling followed by the remaining batter. Zig zag a thin knife once through the loaf to swirl in the filling.
Bake for 45-50 minutes, or until a toothpick comes out clean. Cool in the pan for 15 minutes before removing to a wire rack to cool completely.
Store in an airtight container in the refrigerator for up to 3 days.