Sift together the flour, cinnamon, and the salt into a large bowl. Cut in the butter with a fork until mixture becomes crumbly. Add sugar and vanilla, and mix to a stiff paste. Mix in egg. Knead dough on a floured surface until smooth. Wrap in plastic wrap. Refrigerate for 30 minutes.
Preheat oven to 350*. Grease cookie sheets. Roll out dough thinly and cut into 24 rounds.
Bake 12-15 minutes, or until lightly gold in color. Let cool on wire rack.