Roll each pie crust out onto a floured surface to a rough rectangle about 11 inches square. Cut each pie crust into 12 3-inch rounds. Fit the little pie crust circles into 24 mini pie dishes.
Separate one egg, and place the egg white into a small bowl. Beat the egg white until slightly frothy, and brush the edges of each mini pie crust with egg white. Place the remaining yolk into a bowl, and beat with remaining 2 eggs. Mix the softened cream cheese, sugar, pumpkin, vanilla extract, and pumpkin pie spice into the eggs to make a smooth filling. Spoon about 2 tablespoons of the filling into each crust.
Bake the pies in the preheated oven until the crust edges are golden brown and the filling is set, about 15 minutes. Allow to cool before eating.