In a medium bowl, cream together the sugar and butter. Stir in the coconut extract and the eggs. Combine the flour, baking powder, and salt, stir into the creamed mixture. Finally, fold in the coconut and walnuts.
Divide dough into 2 pieces. Roll each piece out into a log about 10 inches long. Place them on an unprepared cookie sheet and flatten them until they are about 3 inches wide.
Bake for 30 to 35 minutes in the preheated oven, until firm. Cool on baking sheet for 10 to 15 minutes.
Slice the logs crosswise into 1/2 inch wide slices. Place slices cut side down onto the baking sheet.
Return to the oven for an additional 15 minutes, until crisp and light brown. Cool and store in an airtight container.