Sift the flour and fine sea salt together in a small bowl.
Combine the sugar and lavender in the bowl of a stand mixer fitted with a paddle attachment. Mix for 15 to 20 seconds to combine. Add the butter and mix until combined. Mix in the vanilla. Add the flour mixture to the butter mixture and mix on low speed until it forms a soft dough.
Shape the dough into a disk, wrap tightly in plastic, and refrigerate for 20 to 30 minutes.
Line a baking sheet with parchment paper. Roll the dough out to 1/4 inch thick and cut it into 1 1/2- to 2 1/2-inch shapes (circles, squares, or hearts) using a cookie cutter or knife. Place the shapes on the baking sheet, sprinkle with some fleur de sel, and place the baking sheet in the freezer for 15 minutes, until the dough is stiff.
Meanwhile, preheat the oven to 350°F (175°C).
Bake the lavender shortbread cookies for 12 to 15 minutes, or until the edges turn golden brown. Let cool for 5 minutes on the sheet, then transfer them to a wire rack to cool completely. The shortbread keeps for up to 5 days in an airtight container.