In a large bowl, sift together the flour, sugar and salt.
In a separate large bowl, beat the butter with an electric mixer until smooth. Mix in the lavender. Beat in the flour mixture on low speed, just until combined.
Divide the dough into two discs. Wrap in plastic wrap and refrigerate for at least 1 hour, but not more than 8 hours.
Line 2 large baking sheets with parchment paper. On a lightly floured surface, roll the dough to 1/4-inch thickness. Cut into 2-inch circles. Place two inches apart on prepared cookie sheets. Refrigerate cut cookies for 30 minutes to 1 hour.
Preheat oven to 325ºF (165ºC). Bake cookies until the bottom edges are light golden brown, about 12-14 minutes.
Transfer cookies to a cooking rack to cool completely.
Pipe or spread about 1/2 tablespoon of buttercream on the bottom of half of the cookies. Top with remaining cookies.