Preheat oven to 350°F (175°C) and line a cookie sheet with parchment paper or silicone baking mat.
Combine the powdered sugar, vegan butter/coconut oil and salt in a bowl. You can do this by hand with a fork or with an electric hand mixer. Mix together until fluffy.
Add the lavender flowers and lemon zest and stir to combine.
Sieve in the flour and mix by hand until everything is combined. Do not over mix or use electric beaters here.
Add the milk only if you need to to bring the dough together. The dough should be slightly crumbly but hold together if you squeeze it together in your hand.
Lightly dust a surface with flour and shape your dough gently into a ball. Roll out to about 3 - 4 mm thick then use a cookie cutter or mason jar lid to cut into shapes.
Place the cut cookies gently on the prepared cookie sheet, sprinkle with a little granulated sugar then refrigerate for at least 15 minutes until firm.
Remove from the fridge and bake for 10 to 12 minutes. They will start turning a little golden around the edges when done but will still feel soft in the middle.
Leave the cookies on the baking tray for a couple of minutes then carefully transfer to a wire rack to cool completely.
