Using a fine grater or other zesting tool, zest the lemon. Finally chop the herbs.
Cube butter into roughly ½ inch cubes. Put in a large bowl with flour, sugar and half of the lemon zest and herbs.
Gently combine with your fingers to make a soft dough. Roll into 2 cylinders about 2-3" wide and refrigerate for at least 30 minutes.
Preheat oven to 325°F.
Slice cookies ¼" thick and place an inch apart on cookie sheets.
Turn down oven to 275°F and bake until cookies turn a slightly rosy color (just as they begin to brown). Allow to cool completely
Juice the lemon into a small bowl or cup. In a small bowl add powdered sugar and remaining zest and herbs. Thin to desired consistency with lemon juice.
Spoon glaze over each cookie, allow to harden.
Notes
You can make these with any combination of citrus fruit (limes, oranges, tangerines) and fresh herbs (basil, rosemary, lavender, thyme).