In a bowl, beat the butter with an electric mixer until fluffy. Add the brown sugar and granulated sugar; beat until well blended. Beat in the egg and vanilla until thickened. Beat in 2/3 cup of the flour along with the baking soda and salt. Stir in remaining 1 cup flour; the dough will be soft.
Divide the dough in half. Wrap each half in wax or parchment paper or plastic wrap. Shape it into a 6" log. Refrigerate until firm. (The logs can be stored in a plastic bag and refrigerated for up to 1 week or frozen for up to 2 months.) Preheat oven to 350. Using a thin knife, slice each log 1/8" to 1/4" thick. Arrange the cookies 1" apart on a buttered cookie sheet. Bake for 10 to 15 minutes or until lighly golden.
VARIATIONS Ginger Almond: Add 1/2 cup finely chopped crystallized ginger. Roll each log in 1/3 cup of finely chopped blanched almonds.
Lemon Poppyseed: Add 3 tablespoons of poppyseeds and 1 tablespoon of grated lemon zest. Roll each log in 1 tablespoon of poppyseeds.
Spice: Add 1 teaspoon freshly ground nutmeg, 1 teaspoon cinnamon and 1/4 teaspoon ground cloves. If desired, roll each log in 1/3 cup of finely chopped walnuts.
Coffee Edged: Roll each log in 1 1/2 tablespoons very finely group French roast coffee.
Pecan: Add 1 cup finely chopped toasted pecans. Roll each log in 1/3 cup finely chopped toasted pecans.