Preheat oven to 350°F. Line a baking sheet with a silpat or parchment paper.
Mix flour and salt together in a bowl.
In a large bowl, mix together sugar, lavender and zest. Add butter and work together using a rubber spatula. This can also be done in a standing mixer.
Add the flour to the butter/sugar mixture in two additions, and mix until just combined.
Press dough together in a ball and flatten into a disc. Do not overwork. Cover in plastic and refrigerate at least 30 minutes or until firm yet pliable. You can also refrigerate up to overnight. If the dough becomes too tough to work with after refrigeration, set out at room temperature for as long as 30-60 minutes, or until the appropriate texture.
Flour your work surface very lightly. Using a rolling pin, roll dough ¼ inch thick. Cut using a 2 inch round cutter, and place onto the prepared baking sheet. Re-roll the remaining dough and repeat the process. Refrigerate for about 10-15 minutes or until firm.
Bake on the center rack of the oven for about 15-18 minutes or until golden brown. Allow to cool for 5 minutes, then transfer to a wire rack to cool completely.
While the cookies are baking, prepare the lavender cream. In a small pot, bring the cream and lavender to a rapid simmer. Cover and remove from heat. Allow to steep for 20-30 minutes, or until cream tastes strongly of lavender. Cool to room temperature and then refrigerate until ready to use.
While the cookies are cooling, prepare the glaze. Strain lavender cream, saving the lavender flowers for decoration, if desired. In a bowl, whisk together the powdered sugar, 1 ½ tablespoons of lavender cream and 1 tablespoon of milk. Add more milk or cream, based on your desired level of lavender flavor and thickness of the glaze.
If desired, you may decorate the cookies with some of the lavender reserved from the cream. Using tweezers, dip the flowers into the glaze and place on the cookies in any pattern as you prefer. Be cautious not to use too much lavender, as it can be bitter and overpowering. Return cookies to the wire rack until the glaze sets up completely. Enjoy.