In a large mixing bowl, whisk together the flour, granulated sugar, and salt until fully combined.
Create a well in the center of the dry ingredients and add the eggs, milk, melted butter, and vanilla extract. Whisk vigorously until the batter becomes smooth and free of lumps, then let it rest for 15 minutes at room temperature to allow the flour to hydrate.
While the batter rests, prepare the filling by beating the softened cream cheese with an electric mixer on medium speed until creamy, about 2 minutes. Add the heavy cream and powdered sugar, then whip on high speed until stiff peaks form, about 3-4 minutes. Gently fold in the crushed Oreo cookies until evenly distributed.
Heat a 10-inch non-stick skillet or crepe pan over medium heat and lightly grease with butter. Pour 1/4 cup of batter into the center of the pan, immediately tilting and rotating the pan to spread the batter into a thin, even circle. Cook until the edges lift easily and the bottom is lightly golden, about 1-2 minutes.
Flip the crepe using a spatula and cook for another 30-45 seconds until set. Transfer to a plate and repeat with remaining batter, stacking cooked crepes with parchment paper between them to prevent sticking.
Lay one crepe flat on a clean surface and spread 2-3 tablespoons of the Oreo cream filling evenly across the surface, leaving a 1/2-inch border around the edges. Roll tightly into a cylinder shape and repeat with remaining crepes and filling.
Chill the rolled crepes in the refrigerator for at least 30 minutes before serving to allow the filling to firm up slightly for cleaner slicing.