Put butter and sugar in a mixing bowl and beat well with electric mixer.
Add egg, milk, molasses, and vanilla, and mix well.
Add flour, baking soda, salt, and cinnamon and stir. If the dough is too stiff for a mixer, use a sturdy spoon to stir.
Chill one hour or more.
Roll dough into 24 small balls and roll in sugar. Place on baking tray and bake at 350 for 10-12 minutes. Cool on tray for 5 minutes, remove to wire rack and cool completely.
Notes
Do not overbake! Bake for 8 minutes, then check the cookies every 2 minutes until done. Remove cookies from oven when the bottom is just beginning to brown, and the top still looks jiggly and wet in the center. The cookie will sink if you touch it with your finger. Do not stick. toothpick into it - that is not a reliable test for these cookies. Place cookie sheet on a wire rack or hot pads to cool. After 5 minutes, use spatula to remove cookies to wire rack to finish cooling. They will sink down and become flat.