Preheat the oven to 350 degrees F and line a cookie sheet with parchment paper.
In a large bowl, combine the butter and erythritol using an electric mixer, until it is light and fluffy. Add the vanilla and egg white and salt, continue mixing until everything is well combined.
Add the almond flour 1 cup at a time, stirring after each addition, until well mixed. The dough may be a little crumbly, but should stay together if you squeeze it.
Using a rolling pin, Roll the dough between 2 pieced of parchment paper, until it reaches ¼ inch thickness. (you can make a thinner cookie, but be aware that they will be more fragile and you will need to cut down the baking time)
Transfer to the prepared baking sheet, and place in preheated oven for 15-18 minutes, or until they turn a light shade of brown. Remove from the oven and allow them to cool for a few minutes on the cookie sheet before transferring to a cooling rack.
To prepare the glaze, simply combine all the ingredients in a small bowl and mix well. You want a pretty thin consistency, but it should coat the back of a spoon. You can add more almond milk if it seems too thick, or more confectioners erythritol if you feel it is too thick.
Once the cookies have cooled completely, quickly dunk the tops into the glaze and then place them back on parchment paper or the cooling rack until the glaze has dried. You could also just drizzle the glaze over the tops of the cookies.
Notes
*Nutrition info for 1 cookie - 91 calories, 8g fat, 2g carbs, 1g fiber, 3g protein1 net carb! (net carbs = total carbs - fiber)*This nutrition info is only an estimate and will vary based upon the exact brands used for each ingredient as well as the cookie yield.