Combine butter, brown sugar and vanilla in a large bowl. Beat at medium speed, scraping bowl often, until creamy. Reduce speed to low; add flour. Beat, scraping bowl often, until mixture leaves sides of bowl and forms a smooth, soft dough.

Divide dough in half. Shape each half into a 6 x 2 inch round log. Wrap each log in plastic food wrap; refrigerate at least 2 hours.

Preheat oven to 375° F. Cut logs into 1/4-inch slices with sharp knife. Place 1 inch apart onto ungreased cookie sheets. Bake for 7 to 9 minutes or until lightly browned on edges. Let stand 5 minutes before removing from cookie sheets.

Stir together the sugar and cinnamon in a small bowl. Roll warm cookies in cinnamon-sugar mixture.