Preheat the oven to 350°F. Spray a 13x9-inch baking dish with nonstick spray (or rub with butter).
PREPARE THE PUMPKIN BATTER:
In a small bowl, use an electric mixer to combine the cream cheese with the butter until smooth. Beat in the sugar, scraping the bowl occasionally. Beat in the egg, and then add the pumpkin puree, vanilla, cinnamon and ginger. Stir in the flour.
PREPARE THE CHOCOLATE BATTER:
In a medium glass or metal bowl, combine the chocolate and butter. Set the bowl over a saucepan with 1-inch of simmering water and stir occasionally until melted. Remove from heat. In a separate bowl, combine the eggs with the sugar, vanilla and salt. Beat at low speed until light and fluffy- about 4 minutes. Using a large rubber spatula, fold in the melted chocolate. Sift the flour over the batter and fold it in just until combined.
ASSEMBLE THE BROWNIES:
Spread the chocolate batter evenly in the bottom of the prepared pan. Using a tablespoon, drop dollops of the pumpkin batter all over the top. Using the back of a butter knife, swirl the pumpkin batter slightly into the chocolate.
Bake for 25 to 30 minutes (starting checking on brownies at 25 minutes to see if they're done- a toothpick inserted into center should come out clean).
Let the brownies cool completely before cutting.
Notes
Let eggs sit on counter for 30 minutes to achieve "room temperature" eggs.