Add the Oreos to a food processor fitted with the blade attachment. Blend until you have a fine powder, about 30 seconds. Pour the ground Oreos into a mixing bowl and stir in the espresso powder. Set aside.
Loosely cover a 12 cup muffin tin with a few pieces of plastic wrap -- they should be quite large. Now very gently use your hands to push the plastic wrap into each cup -- don't' worry if they don't lay directly against the surface.
Spoon 1 to 2 teaspoons of the Oreo-espresso mixture into each cup.
Soften the coffee ice cream -- either by leaving it out at room temp for about 20 minutes, or in the microwave for about 15 seconds. Evenly distribute the coffee ice cream between the 12 muffin cups, about 1 to 2 tablespoons each. Use the back of a spoon to smooth it out.
Sprinkle this with another couple of teaspoons of the Oreo-espresso mixture.
Place the muffin pan in the freezer until the coffee ice cream has solidified, about 30 minutes. Then repeat this process with the chocolate ice cream, followed by the vanilla ice cream -- but after the vanilla, add the melted butter to the remaining Oreo mixture before adding it to each one. The last ice cream layer might rise above the top of the muffin ring, and that's okay. There will be more of a crust and should have a bit more of the mixture than the inner layers.
Place a piece of parchment paper over the muffin pan and then wrap it tightly with plastic wrap.
Place a baking sheet over this and weigh it down in the freezer. (I use ice packs, but you can also use cans of food.) This will ensure the layers of the mud pie are nicely adhered together. Freeze for at least 30 minutes.
When you're ready to serve, you can cut the plastic wrap around each muffin cup and then gently unwrap the frozen dessert and place it, round side up on a serving plate. They will not be perfect looking!
Drizzle each one with a bit of the Espresso-Chocolate Sauce and serve!