Sift together flour, baking powder, and salt. Set aside.
In large mixing bowl, beat butter at medium speed until light. Gradually beat in sugar; add the egg, vanilla, basil and zest, beating until very light and fluffy.
At low speed, mix in the dry ingredients in three or four additions. Add chopped nuts.
Turn dough out onto a lightly floured surface and divide in half. Shape each half into a roll 6-7" long. Wrap in plastic wrap and refrigerate until firm (approx. 8 hours). (Rolled dough may also be frozen. Thaw frozen dough briefly before baking.).
Preheat oven to 375 degrees F. Cut the dough into 1/4" slices and place onto an ungreased baking sheet about 2 inches apart. Sprinkle lightly with coarse sugar.
Bake 8-10 minutes or until lightly browned. Immediately remove from baking sheet and cool on a rack.