Heat oven to 350°F (325°F for dark or nonstick pan). Grease the bottom of a 9-inch square pan with shortening or cooking spray.
In a small bowl, mix cream cheese and sugar with spoon until smooth. Add pumpkin, flour, cinnamon, nutmeg, and egg white; mix until well blended. Set aside.
Make the brownie batter as directed on the box using the water, oil, egg, and reserved egg yolk. Place 1/2 cup brownie batter in a small bowl; set aside. Spread remaining batter in pan. Spoon filling by tablespoonful dollops evenly onto batter, making 3 rows by 3 rows.
Spoon about 1 tablespoon of the reserved brownie batter in the center of each filling dollop. Draw a knife through the mixture in four straight lines horizontally, then vertically for a swirled design.
Bake 30 to 35 minutes or until toothpick inserted 2 inches from side of pan comes out almost clean. Cool 30 minutes on cooling rack. Refrigerate at least 1 hour until chilled. Cut into 4 rows by 4 rows. Store covered in refrigerator.
