Preheat oven to 350 degrees F or 176 C.

Start by making a rose lemon sugar, where all of your flavor will come from. Do this by grinding up your granulated sugar, rose petals and lemon zest together. I use a mortar and pestle, but a food processor or blender works great too. Add your powdered sugar in as well now and mix.

Cream butter with your rose lemon sugar until well incorporated and fluffy.

Sift in the flour and cornstarch and gradually mix.

You will need to get your hands dirty and really mix well to incorporate all of the butter into the flour. Work it with your hands until the dough becomes a ball. At this point, you can chill the dough if you're not ready to bake, but it's not necessary with this dough.

On a lightly floured surface, roll out dough about 1/2 inch thick. Cut into desired shapes. I used a heart cookie cutter.

Bake for 12 minutes. Longer if you want them golden brown and more crisp (my personal preference) But they should be done and have a nice crumb, and still be pale at 12 minutes if your oven temperature is correct. Let cookies cool on cookie sheets for 5 minutes, then transfer to wire rack.

Let them cool completely and make your icing.

Combine all ingredients in a medium bowl until it has a smooth and runny consistency. If it needs to be thinned more, add a few more drops of milk.

Dip your cookies into the icing after they have cooled.