Preheat oven to 350°F (175°C).
In a mixing bowl, combine gluten-free flour, butter, and sugar for the crust. Mix until crumbly.
Add the beaten egg and mix until the dough comes together. Press into a pie dish.
Bake the crust for 15 minutes or until golden. Set aside.
In a saucepan, heat the milk until warm. In a separate bowl, mix sugar, cornstarch, and gluten-free flour.
Add the dry mixture to the warm milk, stirring constantly until thickened.
Remove from heat and add beaten eggs and vanilla extract. Mix well.
Pour the filling into the baked crust. Sprinkle cinnamon on top.
Bake for 30 minutes or until set. Let cool before serving.