Scrape the cream filling out of the Oreos, place in a bowl, and set aside for later.
Crush the cookie part of the Oreos, mix the crumbs with sugar, and set aside for later.
Bring the water, butter, brown sugar, cinnamon, vanilla extract, and salt to a boil. Add the flour to a separate bowl, pour the heated mixture over it, and mix well. Once the mixture has cooled slightly, stir in the eggs.
Transfer the churro batter to a piping bag with a star-shaped nozzle, pipe flat swirls onto a baking tray lined with parchment paper, and freeze for about 1 hour.
Heat some frying oil to about 350°F and fry the frozen churros for about 3 minutes each. Once they're done frying, roll the warm, fried churros in the Oreo churro coating from earlier.
Whip the heavy cream with the Oreo cream filling you removed earlier. Using a piping bag or a spoon, spread the creamy filling over half of the cooled Oreo churros. Assemble the double stuffed Oreo churros by placing a second Oreo churro on top to make multiple dessert sandwiches.