Preheat the oven to 350°F (175°C).

In a medium saucepan, combine the cooked rice, milk, sugar, and salt. Stir over medium heat until warm but not boiling.

In a mixing bowl, whisk the eggs until well beaten.

Gradually add the warm rice mixture to the beaten eggs, whisking constantly.

Stir in the vanilla extract and cinnamon until fully combined.

Place the pre-made pie crust into the baking dish.

Carefully pour the rice filling into the prepared crust.

Bake the pie for about 45 minutes, or until the filling is set and the top is lightly golden.

Let the pie cool completely before slicing.