Mix together the flour, cardamom powder, and salt.
Cream together the coconut oil and the powdered sugar with a hand mixer or in a stand mixer until it's soft and fluffy, about two minutes.
Add the coconut milk and vanilla and mix well.
Add the flour in three batches, mixing well with a spatula after each addition.
Cover and refrigerate the dough for 15-30 minutes.
Grease an 8 by 8 inch glass baking pan.
Place the shortbread dough in the pan. Press with your fingers into an even layer all the way to the corners of the pan.
Bake the shortbread in a preheated 300-degree oven for 50 minutes or until it is slightly darker at the edges.
Remove to a rack, cool for 10 minutes, and then, using a sharp knife, cut into diamond shapes without going all the way through the shortbread.
Cool thoroughly and then separate into diamond shapes.