In a small mixing bowl, sift together flour, cocoa powder, and crushed Oreos. Set aside.
In a medium saucepan, add water and butter. Bring to a simmer and stir until butter is completed melted. Turn off heat, but leave saucepan on burner and add in flour mixture. Stir until everything is incorporated and becomes smooth dough ball that is uniform in color. The oreo cookie crumbs should melt into the dough completely from the heat of the butter (see notes). Add in eggs and stir into dough until fully mixed. Dough will lose its ball form and become slightly more sticky. Scoop dough into a pastry piping bag.
Preheat oven to 425°F. Line two baking sheets with silicone baking mats. I used a Wilton #12 round piping tip, but if you don't have one, you can also use other round piping tips about 1/2 inch in diameter at the end or you can snip a 1/2 inch off hole on the bottom of your bag. Pipe spiral cookie rounds onto your baking mats, starting in the middle and working your way out. I piped mine to be 2 1/4 inches in diameter. Slightly push in the tail end of your spiral so that it blends into the last outer spiral, making your cookies look more like circles. Space cookies two inches apart.
Bake cookies for about 22 minutes or until they feel crisp to the touch. It's okay if your churros are still in a small pool of oil when you pull them out. The oil will absorb into the mat as they cool.
While churros are cooking, make the filling. In a stand mixer, add butter, vanilla and shortening. Mix on high speed with paddle attachment until it becomes fluffy and light. Gradually add in powdered sugar on low speed until fully incorporated and mixed into the cream filling/frosting.
Add 1/2 cup sugar to a ziploc bag. Once churros are cool to the touch, add a few into the bag, seal the bag and toss until churros are completely coated. Set aside coated cookies and repeat with remaining uncoated churros.
Take half of the churros and flip them onto their back/flat side. Pipe cream filling into the center (I used the same Wilton #12 tip). Place the churro cookies without the cream on top, forming Oreo churro sandwich cookies.