Preheat oven to 325°F.
Line a 13x9x2-inch baking pan with foil, extending foil over the edges of the pan. Grease the foil; set pan aside.
In a medium mixing bowl beat cream cheese and the 1 tablespoon butter with an electric mixer on medium to high speed for 30 seconds. Add the 1/2 cup sugar. Beat until well combined, scraping sides of bowl occasionally. Beat in 1 egg, the pumpkin, 1 teaspoon vanilla, the cinnamon, and ginger until combined. Stir in the 1 tablespoon flour. Set aside.
In a small bowl stir together the 1 1/4 cups flour, the baking powder, and salt; set aside.
In a large saucepan combine the chocolate and 3/4 cup butter. Cook and stir over low heat until melted and smooth. Remove from heat. Gradually add the 2 1/4 cups sugar, beating with an electric mixer on low speed just until combined. Add the 4 eggs, one at a time, beating well after each addition. Beat in milk and the 2 teaspoons vanilla. Gradually beat in flour mixture just until combined.
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. If desired, sprinkle with walnuts.
Bake about 60 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.
To Store: Layer brownies between sheets of waxed paper in an airtight container; cover. Store in the refrigerator for up to 3 days.