1. Beat first 5 ingredients at medium speed with an electric mixer 2 to 3 minutes or until creamy.
2. Add flour; beat until blended. Divide dough into 4 portions, and shape each portion into an 8- x 2-inch log. Wrap in plastic wrap, and chill 1 hour.
3. Whisk together egg and 1 Tbsp. water. Unwrap logs, and brush with beaten egg. Sprinkle turbinado sugar over logs, pressing to adhere, and rewrap. Chill 30 minutes.
4. Preheat oven to 350°. Cut logs into 1/4-inch-thick slices; place 1 inch apart on 2 parchment paper-lined baking sheets. Bake 10 to 14 minutes or until edges are lightly browned, switching pans halfway through. Cool on baking sheets 5 minutes. Transfer to wire racks, and cool.
*Sorghum or honey may be substituted.
Black-Tie Benne Slice 'n' Bakes: Prepare recipe as directed, reducing butter to 1 1/2 cups and adding 1/2 cup each tahini and white sesame seeds to first 5 ingredients in Step 1. Substitute 3/4 cup black sesame seeds for turbinado sugar.
Gingersnap Slice 'n' Bakes: Prepare recipe as directed, reducing salt to 1 1/4 tsp. and adding 2 tsp. ground cinnamon, 1 tsp. ground cardamom, and 1/4 tsp. each ground allspice, ground cloves, and ground nutmeg to first 5 ingredients. Stir in 1/2 cup chopped crystallized ginger after adding flour.
Fruitcake Slice 'n' Bakes: Soak 1 cup candied fruit, 1 tsp. firmly packed orange zest, and 1 tsp. loosely packed lemon zest in 1/4 cup spiced or dark rum 30 minutes. Prepare recipe as directed, stirring fruit mixture into dough after adding flour. Substitute 3/4 cup chopped walnuts for turbinado sugar.
Lemon-Rosemary Slice 'n' Bakes: Prepare recipe as directed, omitting egg and turbinado sugar and adding 1 Tbsp. lemon zest and 2 tsp. minced fresh rosemary to first 5 ingredients. Reduce flour to 3 1/2 cups, and add 1/2 cup cornmeal with flour. Gently toss together warm cookies and 2 cups powdered sugar to coat.