Combine the cookie pieces, sugar, and cinnamon. Add the butter, and stir until combined. 

Spread the cookie mixture evenly on the prepared pan. Bake for 5 to 7 minutes, or until golden brown and crispy. Set aside to cool completely.

Place a 9” x 5” x 3” metal loaf pan or other similarly sized freezer-safe container in the freezer.

Whisk together the condensed milk, cinnamon, vanilla, and salt in a large bowl.

Place the cream in a separate bowl. Use an electric mixer with a whisk attachment to whip the cream at medium-high speed until stiff peaks form.

Fold about 1 cup of the whipped cream into the milk mixture. Transfer that mixture to the remaining whipped cream, and gently fold until combined.

Transfer about a third of the mixture to the chilled pan. Dollop small amounts of dulce de leche over the top. Sprinkle with about a third of the graham cracker mixture. Use a thin knife to swirl gently. Repeat the layers two times. If you like, save a bit of the graham cracker mixture to sprinkle over the top after the ice cream is completely assembled.

Cover and freeze for at least 5 hours, until the ice cream has a scoop-able texture.