First, prepare the cookies. Preheat the oven to 350F and line two baking sheets with parchment or silicone.
In the bowl of a stand mixer fitted with the paddle, beat together the vegan butter and shortening until smooth. Add in the brown sugar, and beat until fluffy.
Finally, mix in the aquafaba and molasses. Beat together until creamy and combined.
Stir in the flour, oats, salt, baking soda, cinnamon, and vanilla, and mix until the cookie dough comes together. It will be kind of soft.
Scoop out tablespoon-sized portions of cookie dough onto your prepared pan. Bake in preheated oven for 15-17 minutes, until cookies have spread and are a toasty brown color.
Set aside to cool completely before assembling.
When ready to make the cookie sandwiches, make the frosting.
In the bowl of a stand mixer fitted with the whisk, beat together the vegan butter and vegan cream cheese until smooth and creamy.
Add in the powdered sugar, a cup at a time, followed by the salt and vanilla. If frosting is too stiff or appears lumpy, add in some nondairy milk until it smoothes out and comes back together.
To assemble, scoop 1 tablespoon of frosting in the center of a cookie, and top with a second cookie. Repeat with all. I was able to make 13 sandwiches.
Serve immediately, or store at room temperature in an airtight container.