To make the cookie chunks, preheat the oven to 350ºF. Line a baking sheet with a Silpat or parchment paper. and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine butter, brown sugar, and granulated sugar on medium speed until light and fluffy. Add the egg and vanilla and mix again until fully incorporated. Add the flour, baking soda, cinnamon, nutmeg, and salt and mix until just combined. Add the oats and pulse until just combined again.
Spread the cookie dough in an even layer about ½ inch thick on the prepared baking sheet. Bake 11-13 minutes or until just starting to brown on the edges and set in the middle. Let cool completely on the baking sheet. Break the cookie into bite sized chunks and transfer to a freezer safe container. Freeze until ready to incorporate into the ice cream base.
Make the Ice Cream
To make the ice cream base, prepare an ice water bath and set aside.
In a medium saucepan over medium heat, combine milk, sugar, maple syrup, and cinnamon. Cook, stirring occasionally, until the mixture just begins to foam around the edges and the sugar has dissolved, about ten minutes (do not boil). Add the cream, vanilla, and salt and stir to combine.
Prop open a gallon size plastic freezer bag (I like to set it in a 4 cup glass measuring cup for stability). Pour the ice cream mixture into the freezer bag, remove most of the air, and seal.
Settle the freezer bag in the ice water bath and allow to rest, massaging the bag once or twice, until cooled, about 30 minutes. Transfer the plastic freezer bag to the refrigerator (I return it to the glass measuring cup) and chill 1 hour or up to overnight.
Stir the mixture slightly then pour into your ice cream maker and process according to manufacturer's instructions. Add the frozen cookie chunks (I used about ¾ of the cookie bites) in the last two minutes of churning or fold in gently with a spatula. Transfer the ice cream to an airtight container and freeze at least 1 hour and up to four days.