Butter an 8-inch square baking pan, for easier removal after baking line bottom and sides with parchment paper. (Butter will help it to stick to pan). Set aside.
For pumpkin layer: Gently mix soft cream cheese and granulated sugar until no lumps remain. Add vanilla and egg and once incorporated add cinnamon, ginger and pumpkin. Set aside.
For brownie layer: Sift together flour, cocoa powder and baking soda and set aside.
Cut butter in pieces and place in bowl large enough to hold all ingredients.
Melt butter over low simmering water and remove from heat. Whisk in sugar. Add eggs and vigorously whisk until well combined. Add vanilla and salt. Remove whisk and using a spatula mix in dry ingredients.
Pour slightly more than half of the brownie mixture into the pan. Cover with all pumpkin mixture and even out smoothly. Cover with remaining brownie mixture. Swirl batter using point of a knife. Bake until the center of brownies has set and no longer trembles, about 35 minutes.
Once cooled flip upside down and flip again. Cut in desired pieces.