Gather all ingredients.

Sift flour, baking soda, and salt into a bowl.

Beat sugar and vegan margarine in a mixing bowl with an electric mixer until creamy, about 2 minutes.

Mix in vanilla. Stir in flour mixture until incorporated, then add coconut milk, 1 tablespoon at a time, until dough comes together.

Wrap dough in plastic wrap and refrigerate for 30 minutes.

Preheat the oven to 350 degrees F (175 degrees C). Line two baking sheets with parchment paper.

Roll chilled dough on a floured surface to a thickness of 1/4 to 1/2 inch. Dip a cookie cutter in flour and cut out cookies, re-flouring as needed. Place cookies onto the prepared baking sheets.

Bake in the preheated oven until just turning golden, about 10 minutes.