Preheat oven to 350° F.
Sift dry ingredients together into a large mixing bowl.
Whisk together the oil, molasses, sugar, milk, and vanilla extract.
Mix wet ingredients into dry, using a whisk, an electric hand mixer, or your hands, until uniform.
Flatten the dough into a disk and refrigerate, wrapped in saran, for 30 minutes (or overnight).
Dust a clean surface with flour. Roll the dough out till it's a scant ¼" thick. Cut into desired shapes.
Bake cookies for 8 minutes, or until the edges are just browning. Let cool before serving.