1. Beat first 3 ingredients at medium speed with a heavy-duty electric stand mixer 2 to 3 minutes or until light and fluffy. Stir in vanilla.
2. Stir together flour and next 2 ingredients in a medium bowl. Gradually add to butter mixture, beating just until blended; stop to scrape bowl as needed. (Do not overmix.)
3. Divide dough in half. Turn 1 dough portion out onto wax paper, and shape into a 10- x 2-inch log. Sprinkle log with 3 Tbsp. Demerara sugar, and roll log back and forth to adhere. Repeat with remaining dough portion and 3 Tbsp. Demerara sugar. Wrap logs in plastic wrap, and chill 2 to 3 hours.
4. Preheat oven to 350°. Cut chilled dough into 1/4-inch-thick slices, and place 1 inch apart on 2 lightly greased baking sheets. Sprinkle 1 1/2 tsp. Demerara sugar over cookies on each sheet.
5. Bake, in batches, at 350° for 12 to 15 minutes or until golden around edges, switching baking sheets halfway through.
6. Transfer to wire racks; cool 5 minutes. Serve immediately, or cool completely. Store up to 4 days.