Prepare and bake the Pastry Crust in a 9-inch round removable-bottom tart pan. Cool crust completely on a wire rack.
Preheat oven to 300°.
Combine 1/2 cup condensed milk and the cream cheeses in a medium bowl; beat at medium speed of a mixer until smooth. Add vanilla, salt, 1 egg, and egg white; beat until combined. Spoon 1/2 cup cream cheese mixture into a small bowl; add 1/4 cup condensed milk, 1 egg, pumpkin, cinnamon, ginger, and allspice, stirring well with a whisk.
Pour remaining cream cheese mixture into prepared crust. Pour pumpkin mixture over cream cheese mixture; swirl together using a knife. Bake at 300° for 50 minutes. Turn oven off; cool tart in closed oven 45 minutes. Remove from oven; cool completely on a wire rack. Cover; chill.