In a small bowl, combine the sugar and cinnamon, set aside.
Make the Cookie Dough:
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter until smooth, about 1 to 2 minutes. Add both sugars and continue beating on medium speed until smooth and creamy.
Scrape down the sides of the bowl, add the vanilla, milk/cream, salt, and cinnamon, and beat until completely combined. Add the flour and beat on low until just combined, about 1 minute. Add more milk/cream, if dough seems too dry. Chill dough for 30 minutes.
Break dough up into teaspoon-sized pieces and place onto a plate. Roll each piece of dough into the cinnamon-sugar, then place them back onto the plate and into the freezer while you make the ice cream.
Make the Ice Cream:
In a medium bowl, whisk the sweetened condensed milk, pumpkin, brown sugar, vanilla, and spices together until combined; set aside.
In the chilled bowl of a stand mixer fitted with a whisk attachment, whip the heavy cream until stiff peaks form. Fold a cup of the whipped cream into the pumpkin mixture to lighten it up. Then add the lightened pumpkin mixture into the rest of the whipped cream, folding everything together until combined.
Stir 3/4 of the snickerdoodle dough pieces into the ice cream, then pour ice cream into a freezer-safe container. Top with the remaining cookie dough pieces, then chill ice cream in the freezer for at least 6 hours or overnight. Scoop and enjoy!
Notes
*If you’re a little wary of consuming raw flour, you have the option of heat-treating it in the microwave or the oven. (See notes above)