Preheat oven to 350 degrees and line baking sheet with parchment paper.

To a mixing bowl, add coconut flour, classic monk fruit sweetener, shredded coconut, cream of tartar, and baking soda. Whisk until all ingredients are fully incorporated. Add beaten eggs, coconut oil, and vanilla extract. Mix with an electric mixer until wet and dry ingredients are well-combined.

Form dough into 8 equal balls and place on the prepared baking sheet, lightly pressing down on the dough to flatten. Bake until edges are golden brown, about 18-20 minutes. Remove from oven and transfer to a cooling rack.

While cookies cool, for the glaze, pulse monk fruit sweetener in blender or food processor until powdered. Melt coconut oil in the microwave and, once melted, add to powdered monk fruit sweetener. Pour in 2 tbsp coconut milk and pulse in a blender until well-combined and a glaze forms. If glaze mixture is too dense, add additional tbsp of coconut milk. Transfer glaze from blender to shallow dish or plate. Carefully dunk the top of cookies in glaze and set on a cooling rack to harden.