Preheat your oven to 350 °F and line a baking sheet with parchment paper or a silicone baking mat.
Prepare your flax egg by whisking together 1 tablespoon of ground flaxseed with 3 tablespoons of water. Set aside to thicken.
In a large bowl, mix together the melted coconut oil and sugar until combined.
Add in the pumpkin puree, vanilla and thickened flax egg and mix until smooth.
In a separate bowl, whisk together the dry ingredients, from the flour to the salt. Add the dry ingredient into the wet ingredients and mix until a sticky, thick batter forms.
Drop the batter by heaped tablespoon amounts onto your prepared baking sheet.
Bake the cookies for about 18 minutes or until the bottoms turn golden brown.
Remove the cookies from the oven and allow them to cool while you prepare the frosting.
To make the frosting, whisk together the powdered sugar, non-dairy milk, coconut oil and vanilla until a smooth frosting forms. If it's too thick you can add more non-dairy milk 1 teaspoon at a time until it reaches your desired consistency.
Either dip the top of the cookies into the frosting or use a spoon to spoon 1-2 teaspoons worth of frosting over each cookie.
Allow the frosting to harden and then serve!
Notes
If you want to freeze these, I recommend not frosting them until thawing and serving.