Preheat oven to 350 degrees, and line a baking sheet with a layer of parchment paper.
In your stand mixer, cream together the vegan butter with the sugars for about 3 minutes, until light and fluffy.
Add the vanilla and coffee and mix to combine.
Whisk together the dry ingredients in a separate bowl.
Add half the dry ingredients to the butter/sugar mixture and mix briefly. Add half the oat milk and mix again.
Repeat with the remaining dry ingredients and the oat milk.
Scrape down the sides of the bowl and mix again. The batter will be quite thick.
Drop the batter in dollops all over the prepared cookie sheet, then using an offset spatula, spread it all over, trying to make it as even a layer as possible.
Bake in preheated oven for about 10 minutes, until it is dull.
Remove from oven and allow to cool.
Use a cookie cutter or just a knife to cut the cookies into your desired shape. Place the cookies, top side down, on your work surface, and dollop the ice cream on top. Top with another cookie and smoosh them down together.
Place in the freezer to refreeze for a few hours or overnight.