Preheat oven to 350F.
Make a flax egg by mixing together the flaxseed and water in a small bowl. Set aside to thicken.
In a stand mixer or with a hand mixer, cream the room temperature butter. Add the brown sugar. Keep mixing until the butter is thick and creamy.
Then, add in the molasses and flax egg. Mix on low.
Whisk together the all purpose flour, baking soda, cinnamon, and salt in a bowl.
Slowly add the dry mixture to the creamed butter mixture. Once combined, turn off mixer.
With a spatula, mix in the oats and chocolate chips.
Line 2-3 baking trays. You will probably need to bake 2-3 batches depending on how big your baking tray is.
Using a large cookie scoop or measuring cup, scoop out 3-4 tbsps of cookie dough and roll in to a ball. Place on baking sheet and flatten slightly with the palm of your hand. Continue with the rest of the dough, leaving about 3in between each cookie. For smaller cookie sandwiches, use 2 tbsps of cookie dough.
Bake cookies for 15-17 minutes or until slightly brown around the edges but still soft in the center.
Allow cookies to cool on baking sheet for 5 minutes then transfer them to a wire cooling rack.
When the cookies are cool, start on the frosting.
In a stand mixer or with a hand mixer, cream the room temperature butter. Slowly add in the powdered sugar, vanilla, cinnamon, and the non-dairy milk. Turn off mixer once the frosting is smooth and creamy.
Use a piping bag or a spatula to spread on an even layer of frosting to one side of the cookie and place another cookie on top creating the sandwich.