Preheat oven to 325 degrees F. Line a 13x9 baking pan with foil, extending foil over the edges of the pan. Grease the foil; set pan aside.
The Pumpkin Cheesecake
In a medium mixing bowl or the bowl of your stand mixer beat the cream cheese and the 1 tablespoon butter on medium for 30 seconds.
Add 1/2 cup sugar. Beat until well combined.
Beat in the egg, the pumpkin, vanilla, the cinnamon, and ginger until combined.
Stir in the 1 tablespoon flour. Set aside.
The Chocolate Brownie
Coarsely chop the unsweetened chocolate.
Melt the butter and chocolate in a saucepan over low heat. Stir and melt until smooth.
Beat the eggs and sugar at medium speed with a stand mixer or a hand mixer. Beat until the mixture is well blended.
Once the chocolate is melted, turn the mixer down to low and slowly drizzle the chocolate into the mixture. Continue to blend until the chocolate is fully mixed in.
With the mixer still on low, gradually add the flour and vanilla until fully incorporated.
Put it all Together
Spread chocolate mixture evenly in the prepared pan. Spoon cream cheese mixture in several mounds on top of the chocolate batter. Using a narrow metal spatula, gently swirl the cream cheese mixture into the chocolate batter.
Bake about 40 minutes or until center is just set when pan is gently shaken. Cool in pan on a wire rack. Use foil to lift uncut brownies out of pan. Cut into brownies.