Make the brown sugar and cinnamon ice cream: Prepare an ice bath in the sink or in a large heatproof bowl.
In a medium saucepan, combine the brown sugar, skim milk powder, cinnamon, and milk. Stir with a hand mixer or whisk until smooth. Make sure the skim milk powder is wholly dissolved into the mixture and that no lumps remain (any remaining sugar granules will dissolve over the heat).
Clip a candy thermometer to the saucepan and set the pan over medium heat. Cook, stirring often with a rubber spatula and scraping the bottom of the pan to prevent sticking and burning, until the mixture reaches 110°F (45°C), 5 to 10 minutes. Remove the pan from the heat.
Place the egg yolks in a medium bowl. While whisking, slowly pour ½ cup (120 ml) of the hot milk mixture into the egg yolks to temper them. Continue to whisk slowly until the mixture is an even color and consistency, then whisk the egg-yolk mixture back into the remaining milk mixture.
Return the pan to the stovetop over medium heat and continue cooking, stirring constantly, until the mixture reaches 165°F (75°C), 5 to 10 minutes more.
Transfer the pan to the prepared ice bath and let cool for 15 to 20 minutes, stirring occasionally. Add the vanilla and stir to combine.
Pour the ice cream base through a wire-mesh strainer into a storage container and place in the refrigerator for 1 to 2 hours, or until completely cool.
Make the oatmeal cookies: Preheat the oven to 350°F (175°C). Butter a 12-by-18-inch rimmed baking sheet and line it with parchment paper.
In a large bowl, toss together the oats, flour, sugar, and salt.
In a separate small bowl, whisk the eggs and vanilla together until smooth. Add the butter and whisk to combine. Pour the egg mixture over the oats. Work the dough together with your hands until there are no dry clumps of oats or flour left in the bowl.
Spread the mixture in an even layer across the prepared baking sheet (as if you were making a tray of brownies). At the shop, we cook them about ½ inch (12 mm) thick so that we can easily drop them into bite-size pieces. Bake for 20 to 25 minutes, until the top is a deep golden brown. Let cool, then chop the cookies into small pieces and set aside.
Transfer the cooled base to an ice cream maker and churn it according to the manufacturer's instructions.
Transfer the ice cream to a storage container, folding in the oatmeal cookie pieces as you do. Use as many of the cookie pieces as you want; you won't necessarily need the whole batch. Serve immediately or harden in your freezer for 8 to 12 hours for a more scoopable ice cream.