In a large bowl, whisk the flour, baking soda, baking powder, salt, and spices together. Stir in the oats; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream the butter until smooth. Add both sugars and beat until pale and fluffy. Add the eggs, egg yolk, and vanilla, and beat until smooth. Dump in the flour mixture, mixing until just combined. Wrap dough in plastic wrap and chill in the refrigerator for at least 2 hours.
Preheat the oven to 350ºF and line a baking sheet with parchment paper. Using greased hands, roll dough into 1-inch balls, about 2 Tablespoons of dough per cookie. Place dough balls onto prepared baking sheet, leaving 2 inches of space between each one.
Bake for 8-10 minutes, or until lightly browned around the edges. Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Make the Ice Cream:
Line a 9x13-inch pan with aluminum foil; set aside.
In a large bowl, whisk the sweetened condensed milk, vanilla, cinnamon and salt together until smooth; set aside in the refrigerator.
In the chilled bowl of a stand mixer fitted with the whisk attachment, whip the heavy cream on high until stiff peaks form. Add 1/4 of the whipped cream to the sweetened condensed milk mixture, stirring until combined. Add the rest of the whipped cream, using a rubber spatula to fold until just combined. Pour ice cream into the lined pan, using a spatula to spread it into an even layer. Chill in the freezer for at least 4 hours.
To Assemble:
Pair each oatmeal cookie up with a similar size cookie. Remove the frozen ice cream slab out of the freezer and use a glass or biscuit cutter to cut circles out of the ice cream. Place ice cream round on top of the bottom-side of a cookie and top with another cookie. Repeat with the remaining ice cream and cookies.
Chill ice cream sandwiches in the freezer for 30 minutes before wrapping individually in plastic wrap and storing in a freezer-safe ziplock bag.