(Adapted from Martha Stewart's Sugar Cookie Recipe, Msl February '96)
Sift together flour, salt and baking powder and set aside. In mixer, cream butter and sugar till fluffy. Beat in eggs. Add flour mixture and mix on low till thoroughly combined. Stir in vanilla, lemon juice, zest and basil. Roll dough into two logs and chill for 30 minutes. Slice cookies approx 1/4 inch thick and bake at 325 approx 15 minutes, till slightly brown around the edges. Frost with lemon/lime glaze - see below.
This part isn't very specific. I just mix small amts fresh squeezed lemon or lime juice with powdered sugar until smooth and spreadable. Spread on cookies. Get some tea and enjoy!