Preheat oven to 350 degrees F (175 degrees C). Line a 11x15-inch baking pan with aluminum foil.
Combine flour and brown sugar in a bowl. Cut in butter using a pastry blender or 2 forks until crust mixture is crumbly. Press 2/3 of the mixture evenly into the prepared baking pan.
Bake crust in the preheated oven until lightly browned, about 15 minutes. Let cool, about 10 minutes.
Combine cream cheese, pumpkin puree, and white sugar in a bowl; beat with an electric mixer until smooth. Beat in eggs one at a time. Stir vanilla and pumpkin pie spice into the filling mixture. Pour over the cooled crust.
Mix reserved crust mixture and walnuts together in a small bowl make streusel topping. Sprinkle streusel topping over the filling.
Bake in the preheated oven until filling is set, 40 to 45 minutes. Refrigerate until firm, at least 2 hours. Cut into bars.