Sift together the flour, baking soda and salt. Using an electric mixer, in a large bowl, beat the butter with 1/4 cup of the granulated sugar and the brown sugar at medium speed until combined. Add the egg and vanilla and beat until pale. Stir in the dry ingredients just until combined. Divide the dough into thirds and wrap in plastic wrap. Shape the dough into 6-inch logs and refrigerate or freeze until firm.
Preheat the oven to 350°. In a small bowl, combine the remaining 1/2 cup of granulated sugar with the cinnamon and spread on a flat plate. Unwrap the logs and roll them in the cinnamon sugar until thoroughly coated. Rewrap the logs and refrigerate or freeze until firm.
Slice the cookie dough logs 1/4 inch thick. Arrange the slices 1 inch apart on 2 large cookie sheets and bake for 18 to 20 minutes, or until golden. Transfer the cookies to a rack to cool and bake the remaining cookies. Serve the cookies when they have cooled.
The cookie dough logs can be frozen for up to 2 weeks. The baked cookies can be kept in an airtight container for up to 2 weeks.