In a medium bowl, stir together sweetened condensed milk, vanilla extract, and cinnamon. Set aside.
In the bowl of a stand mixer, using the whisk attachment, beat cream on high until stiff peaks form, about 3 minutes. With a rubber spatula, gently fold whipped cream into the sweetened condensed milk mixture. Stir in 1 1/4 cups of the snickerdoodle cookie pieces.
Pour ice cream mixture into a loaf pan or container. Smooth with a spatula and sprinkle remaining cookie pieces over the top. If desired, sprinkle a little cinnamon sugar over the top too. Cover with plastic wrap and freeze until firm, about 6 to 8 hours.
When ready to serve, remove from freezer and scoop away!