In a large bowl, whip butter and sugar together until creamy.
Whip in the egg, then the flour and the salt and continue to whip until the dough starts to form large crumbles.
Whip in the lavender, then transfer the dough onto a large work surface and knead into a ball.
Cut the ball in half, shape into two disks, wrap them tightly in plastic wrap and chill in the fridge for 30 minutes.
Heat the oven to 350 degrees F. Roll out the dough on a lightly floured surface, then cut out the cookies. Set the cookies onto two* large baking sheets lined with parchment paper or silicone baking mats. (You can set them very closely together, they won't spread very much at all.)**
Bake the cookies until lightly browned (about 14 minutes), then let them cool.
For the glaze:
Whisk powdered sugar and lemon juice together. (Adjust with more powdered sugar or lemon juice until you have a thick but spreadable consistency.)
Spread the glaze onto half of the cookies and let dry.
For the filling:
Whip all ingredients together until creamy and fluffy.
Spread a dollop of filling onto each unglazed cookie. (Use about 1 teaspoon of filling for a 2-inch diameter cookie.)
Top with a glazed cookie.
Notes:
*If you only have one sheet, roll out and bake only half of the cookies at a time. (Be sure to let the sheet cool down to room temperature before setting the second batch of cookies on.)**To bake two sheets at the same time, set one sheet on a rack right below the middle of the oven and the second one right above the middle. Switch the positions of the baking sheets (both top to bottom and front to back) halfway through the baking time.