In a medium mixing bowl, whisk together the pumpkin puree, pumpkin pie spice, milk, and pudding mix until the mixture is smooth and no lumps remain.

Add the frozen whipped topping to the bowl. Use a spatula to gently fold it in until the filling is light, fluffy, and fully combined.

Spoon the filling into the graham cracker crust, then spread it out evenly to the edges.

Cover the pie loosely with plastic wrap and place it in the refrigerator for at least 4 hours, or until the filling is set and firm enough to slice.

When ready to serve, top with extra whipped cream if you like, and cut into slices.