Line a baking sheet with parchment paper or silicone baking mat. Set aside.
In a large mixing bowl, combine butter and sugar and mix with electric mixer until fluffy, about 2 minutes.
Add cinnamon and vanilla and mix until combined.
Add flour and mix. The dough will look crumbly but it will come together.
Divide the dough in half, wrap each half in waxed paper, flatten into a disk and refrigerate for at least 1 hour.
Preheat oven to 300 degrees F.
Unwrap each disk and place on lightly floured surface. Roll out into 1/4 inch thick circle. Cut out cookies. Place them on prepared baking sheet.
Bake cookies for 24 to 28 minutes, or until they start to brown on the edges.
Cool on sheet for 2 minutes, transfer onto a wire rack to cool completely.