To make the ice cream base:

1. Take half of the Oreo cookies (about 13-14) and use a butter knife to split them in half. Scrape the creme filling into a small bowl and add the chocolate cookie halves to a medium mixing bowl (I used a 3 quart size.)
2. Cover the small bowl of creme filling and set it aside. In a small saucepan, combine the milk, sugar, salt and vanilla extract. Set the saucepan over medium low heat, stirring occasionally until the sugar and salt have dissolved, about 5 minutes. 
3. Remove the saucepan from the heat and stir in the 1 1/2 cups of heavy cream. Pour the milk/cream mixture over the chocolate cookie halves in the medium-large bowl, using your fingers to push them down into the milk. The cookies will float, but just make sure that they’ve all been dunked and coated at least once.
4. Cover the milk and cookies, and chill for at least 4 hours. In the meantime, make the sandwich squares.

Make the chocolate sandwich squares

1. Preheat the oven to 350 degrees and line a 9 x 9 square pan with parchment paper. See the post for the best way to line the pan and make assembly easier. You will need 2 squares of parchment paper for the entire process, since you need to make 2 square cookies for the top and bottom. Set the prepared pan aside.
2. Sift the flour, cocoa powder, salt and baking soda together in a bowl and set aside.
3. Combine the butter and both sugars in a large mixing bowl. Use a spatula to mix them until you have a thick paste. Add the dry ingredients and milk all at the same time, using the spatula to gently work them together until you have a thick “batter.” It won’t be as thick as a traditional cookie dough, but it also won’t really be pourable.
4. Divide the batter in half and add the first half to the prepared square pan, leaving the remaining batter in the bowl. Use a small offset spatula or butter knife to spread the batter into an even layer.
5. Bake the square for 8-9 minutes, or until the top is no longer wet and shiny. Remove the pan from the oven and firmly tap it 5 times on the counter to settle the cookie, but don’t shut the oven off. Allow the cookie to cool for 10 minutes, then chill the pan in the freezer for another 10 minutes.
6. At this point, the pan and cookie should be at room temperature. Gently lift the cookie out of the pan by grabbing the corners of the parchment paper, and quickly transfer it to a wire rack.
7. Re-line the square pan with the second square of parchment and add the remaining half of the batter. Smooth the surface and bake for 8-9 minutes. After baking the second cookie, you can shut the oven off.
8. Don’t remove the second baked square from the pan, since it’s the first layer in assembling the sandwiches. Wait to proceed with the rest of the recipe until the cookie halves and milk have had the full 4 hours to soak in the fridge.

Assemble the sandwiches:

1. Add the remaining 2 tsp of heavy cream and tsp of corn syrup to the small bowl of creme filling. Microwave on full power for 15 seconds, and whisk well until the mixture is smooth. Pour the creme over the chocolate square in the pan, and use a small offset spatula or butter knife to smooth it evenly over the surface.
2. Chill the pan while the ice cream is churning.
3. Remove the soaked cookie halves and milk from the fridge. Use a whisk to stir the mixture and break up the softened cookies. This shouldn’t take more than a few seconds, since the cookies will be fully softened in the milk. Whisk gently until there are no big chunks of cookie remaining.
4. Churn the cookie/milk mixture in your ice cream maker, according to the manufacturer’s instructions. Once the ice cream reaches a soft serve texture, add the Oreo cookie chunks and allow them to fully mix into the ice cream.
5. Spread the ice cream over top of the creme and cookie layer in the pan, and quickly top the ice cream with the second chocolate cookie square. It should be firm enough from the freezer to not break or bend.
6. Cover the pan with a sheet of plastic wrap, and freeze overnight or until firm.
7. Once firm, cut the slab into individual sandwiches, and decorate the sides with sprinkles, if desired. The sandwiches will be soft enough to eat right out of the freezer!