Preheat oven to 350.
Butter and flour a 9-inch cake pan.
In a stand mixer beat butter for 30 seconds.
Add sugar and beat for a minute.
Add eggs, one at a time, beating after each.
Add extract, baking powder, and salt, beating well.
Turn mixer to stir and add half of flour.
Add coconut milk and stir.
Add remaining flour, stirring until blended.
Add batter to prepared cake pan.
Bake for 30 minutes or until toothpick inserted in center comes out clean.
Cool for 10 minutes in pan; remove cake from pan and cool completely.