Prepare the Baking Equipment: Preheat the oven to 220°C (425°F). Line a 12-cup standard muffin tin with paper muffin liners and set aside.
Prepare the Oreo Streusel Topping: In a small mixing bowl, combine the softened unsalted butter, granulated sugar, all-purpose flour, and salt. Add the crushed Oreo cookies and, using a fork or clean fingers, mix until the mixture resembles coarse crumbs. Set aside.
Prepare the Dry Ingredients: In a medium-sized mixing bowl, whisk together the all-purpose flour, cocoa powder, baking powder, baking soda, and salt. Ensure all dry ingredients are evenly incorporated. Set aside.
Prepare the Wet Ingredients: In a separate large mixing bowl, combine the granulated sugar, sour cream, vegetable oil, milk, eggs, and vanilla extract. Whisk thoroughly until the mixture is smooth and homogenous.
Combine the Wet and Dry Mixtures: Gradually incorporate the dry mixture into the wet mixture, folding gently using a spatula or large spoon. Mix only until the dry ingredients are just moistened; overmixing should be avoided to prevent the muffins from becoming dense.
Add the Chopped Oreos: Once the batter is uniformly combined, gently fold in the chopped Oreo pieces, ensuring even distribution throughout the mixture.
Portion the Batter: Divide the batter evenly among the prepared muffin cups. Each cup should be filled close to the top to yield tall, bakery-style muffins. Generously sprinkle the prepared Oreo streusel topping over each filled cup.
Bake the Muffins: Place the muffin tin into the preheated oven and bake at 220°C (425°F) for 5 minutes. Without opening the oven, reduce the temperature to 180°C (350°F) and continue baking for an additional 18–20 minutes, or until a toothpick inserted into the center of a muffin emerges clean or with a few moist crumbs.
Cool the Muffins: Remove the muffins from the oven and allow them to cool in the tin for approximately 5 minutes. Thereafter, transfer them to a wire rack to cool completely before serving.