Preheat the oven to 350°F/180°C. Line 4 baking sheets with parchment paper or a non-stick surface. Set the oven racks to the middle of the oven.
Make the flax egg. Combine the flaxseeds with hot water. Mix and set aside for 5 minutes.
Make the dough. Start with the wet ingredients in a large bowl with a hand mixer or in the stand mixer with the paddle attachment. Cream the softened vegan butter with brown sugar and white sugar. Add the vanilla, molasses, and flax seed egg. Now add the quick oats, flour, baking soda, baking powder, cinnamon, and salt. Mix until the dough is formed.
Shape the cookies. Using a tablespoon, scoop the cookie dough into balls. Place the cookie dough ball onto the baking sheet, 12 to a tray, gently pressing the tops down to form a cookie dough disc. Repeat with the remaining dough. You should get about 45 cookies.
Bake the cookies. Bake the cookies for 13 to 15 minutes or until the edges are lightly browned. Remove them from the oven and let them rest for 10 minute on the hot baking trays before removing them to a cooling rack to cool completely before icing.
Frost the cookies. In a small bowl, mix together the powdered sugar, water (or dairy free milk), and vanilla until the icing is smooth. Take a spoonful and spread the icing over top of each cookie. Repeat for the remaining cookies. Let them dry on a cooling rack. Serve and enjoy!
