Heat the oven to 180 °C / 350 °F and line a baking sheet with parchment paper. Have the pan ready before shaping because the dough is easiest to handle once it has rested.

Combine the coconut flour, softened butter or coconut oil, large eggs, vanilla, and granulated sweetener in a mixing bowl with a fork. The mixture will quickly thicken as the coconut flour starts absorbing the liquid.

Knead the mixture by hand until it becomes a smooth, unified dough, then let it stand for a few minutes before gathering it into one large ball. The dough should feel pliable and hold together without cracks; if it is too soft to shape, refrigerate the bowl for 15 to 20 minutes.

Divide the dough into 16 equal portions and roll each portion into a ball. Arrange the balls on the lined baking sheet, then press each one into a thick disc about 4 cm wide and 1.5 cm thick.

For the optional finish, whisk the remaining egg with the milk or cream and brush the mixture over the shaped cookies. The surface should look lightly coated, not drenched, before it goes into the oven.

Bake for about 13 to 15 minutes. Remove the cookies when the edges are lightly golden and small surface cracks begin to appear.