In a medium-sized bowl, whisk together the vanilla and the instant espresso to dissolve the granules. Add in the condensed milk and kosher salt, set aside.

In a large bowl, add the cold heavy cream. Using a hand mixer, beat on low speed until stiff peaks form, about 4 minutes.

Pour the condensed milk mixture into the heavy cream and use a spatula to gently fold the ingredients together until completely combined.

Heat the cream and corn syrup. Cook the cream, corn syrup, and salt in a small pot over medium-high heat until the cream begins to simmer, stirring to dissolve the glucose. Remove the cream from the heat and set aside in a warm place. Place the butter near the stove.

Caramelize the sugar. Place the sugar and water in a small heavy-bottomed saucepan, and stir gently. Place the pot over medium-high heat, and use a moist pastry brush dipped in clean water to wash down stray sugar crystals so they dissolve in the boiling sugar. Continue cooking, washing down any crystals, until the sugar reaches a medium amber. Dip a piece of white paper in the caramel to test the color.

Mix the cream into the caramel. When you have reached caramel color, immediately remove the pot from heat and stir in the butter to stop the cooking. Add the warm cream bit by bit, being careful as it will sputter. Add the vanilla and stir. If there are any lumps of unmelted caramel, continue cooking the sauce at a low simmer until smooth and even.

Add oreos and salt to food processor and pulse until crumbs form. Turn food processor to its continuous setting and let run until mixture is becoming smooth. Add in oil one tablespoon at a time, processing in between each addition and then add in the butter, followed by the milk. Add in the water, if using. Scoop out of food processor and place into a sealed container. Mixture will stay in refrigerator, in sealed container for 10 days.

Using a 9x5 loaf pan, layer 1/3 of the coffee ice cream, then drizzle with caramel, dollop with oreo butter, and sprinkle with chopped oreos. Repeat with the next 1/3 of the ice cream and the same layers of caramel, oreo butter, and chopped oreos. Finish with the remaining 1/3 of the ice cream, topped with a final layer of caramel, oreo butter, and chopped oreos.