In a medium sized bowl using beaters, or in the bowl of a stand-mixer with paddle attachment, beat the vegan butter and brown sugar together until smooth. Blend in vanilla, salt and milk. Stir in the flour, and then the mini chocolate chips.
Line an 8"x 8" baking pan with parchment paper, leaving enough hanging over 2 opposing sides so you have paper handles to lift the dough out later. Divide the cookie dough in half and press half of it into the baking pan. Use a base of a dry measuring cup or a silicone spatula to flatten the dough. Place another piece of parchment paper over the first cookie dough layer leaving some hanging over the sides of the pan. Press in the rest of the dough evenly like you did for the first layer. Fold the parchment handles over the cookie dough, and place in the freezer for about 2 hours or until frozen through.
For the Caramel:
Combine all of the ingredients for the caramel except for the vanilla in a small pot over medium heat. Whisk constantly until the mixture is melted and smooth. Once boiling, let cook for one minute then remove from the heat. If you cook it too long it may turn into chewy caramel once cooled which is hard to swirl. Remove from heat and carefully whisk in the vanilla – it may bubble and sputter. Once cool enough to safely store in glass, pour it into a jar and let come to room temperature.
For the Vanilla Ice Cream:
In a medium sized pot, whisk together the coconut cream, sugar, cornstarch and salt. Turn on the heat to medium, whisking often to prevent sticking or burning. Bring to a boil, let cook one more minute and then remove from heat and whisk in the vanilla. Pour into a heat safe bowl and place a piece of plastic wrap directly over the custard to prevent a skin from forming. Once cool enough, place in the fridge until completely chilled.
If you have an ice cream maker, follow the manufactures instructions for churning once the custard has completely chilled. If you don't have an ice cream maker, proceed to assembly.
To Assemble the Ice Cream Sandwiches:
Once the cookie dough is frozen, the custard is completely chilled (and churned if you have an ice cream maker) and the caramel is at room temperature, you can assemble your ice cream sandwiches!
Remove the cookie dough from the freezer. Carefully lift the top layer of cookie dough out of the pan using the ends of the parchment to lift. If you discover you didn't evenly cover the bottom layer and now your two layers are stuck together, lift both layers out of the pan, and use a knife to carefully and gently separate the two. Place the first layer back in the pan.
Pour the vanilla ice cream base over the cookie dough, and smooth out. Drizzle about 1/2 cup of the caramel over the ice cream and, using a toothpick or knife, create some swirls in the caramel. Don't over do it, or you'll mix the caramel in without any distinct swirls. Save the rest of the caramel for another use.
Carefully place the second layer of cookie dough over the ice cream. If the ice cream is starting to melt, don't press down very hard, just make it as level as possible. Quickly get it back into the freezer to set which takes 5-8 hours depending on the freezer and if you'd churned your ice cream.
Using the parchment paper handles, lift the cookie dough ice cream out of the pan and place on a cutting board. Using a large, sharp knife, cut into 12-16 squares and enjoy! Leftovers should be wrapped airtight, and frozen.
*flour should be heat treated before being consumed. Spread it out evenly on a large baking sheet and bake at 350°F for 5-7 minutes, or until it reaches 165°F, stirring once for even heating. Keep an eye on it so it doesn't burn. Whisk and bring to room temperature before making the cookie dough.**use full fat canned coconut milk (or coconut cream if you can find it). Avoid those with gums or additives. Chill the cans overnight in the fridge to easily scoop out the coconut cream, leaving the water behind for another use.