In a medium bowl mix flour, ground lavender buds, lemon peel and salt. Set aside.

In a large mixing bowl beat the butter with an electric mixer on medium to high speed for 30 seconds. Add the powdered sugar and milk and beat until its thoroughly mixed well.

Beat in as much of the flour mixture as you can with the electric mixer. Finish stirring in what flour you have left by hand if needed.

On a floured surface roll the dough into a 10 inch log. Wrap the dough in plastic wrap or parchment paper and chill until the dough is firm. (2 to 24 hours)

Once dough is chilled, preheat oven to 350°. Cut the dough roll into 1/4 inch slices and put the slices onto a parchment paper lined cookie tray.

Bake for 10 minutes until the edges are slightly browned. Cool either on parchment paper or on a wire rack.