Prepare Basic Sugar Cookie Dough as directed, except add rosemary and lemon peel with the sugar.
Divide dough in half and tightly wrap each piece with plastic wrap and chill for 1 hour or until dough is easy to handle.
On a lightly floured surface, roll half the dough (keep remaining dough in refrigerator) into a 16x10-inch rectangle. Using a fluted pastry wheel, cut each rectangle lengthwise into eight 1-1/4-inch strips. Cut strips crosswise into 4-inch pieces. Place about 1 inch apart on ungreased cookie sheets. If you like, curve pieces slightly. Continue as directed in step 5.
On a lightly floured surface, roll half the dough (keep remaining dough in refrigerator) until 1/4 inch thick. Using a 2-1/2x1-3/4-inch diamond-shaped cutter with fluted sides, cut out dough. Place about 1 inch apart on ungreased cookie sheets.
Bake in 375 degree F oven for 6 to 8 minutes or until edges are firm when lightly touched and bottoms are very lightly browned. Cool on cookie sheet for 1 minute. Transfer cookies to wire racks; cool. Makes 64.
To decorate, in a small bowl, combine powdered sugar, milk, and lemon juice. Stir in additional milk, 1 teaspoon at a time, until drizzling consistency. Drizzle a very thin line of glaze in a zigzag pattern over tops of cookies. Let set before serving.