In a large bowl, beat the butter until fluffy. Add the brown sugar and granulated sugar and beat until well blended. Add the egg and vanilla and beat until thickened. Beat in the melted chocolate, then add 3/4 cup of the flour along with the baking soda and salt. Stir in the remaining 1 cup flour to make a soft dough. Proceed as directed in Steps 2 and 3 of the Brown Sugar Icebox Cookies.
For the Double Chocolate and nut variations, add the extras with the final portion of flour. Roll the logs in the nuts before chilling.
Add 1 teaspoon pure peppermint extract to the dough with the vanilla.
Add 2 ounces chopped semisweet chocolate.
Add 2/3 cup finely chopped unsalted macadamia nuts. Roll each log in 1/3 cup finely chopped macadamias.
Add 1 cup finely chopped, toasted and peeled hazelnuts. If desired, roll each log in 1/3 cup finely chopped hazelnuts.
Add 1 cup finely chopped unsalted roasted peanuts. If desired, roll each log in 1/3 cup finely chopped peanuts.