Step 1 In the bowl of a stand mixer with the paddle attachment, or in a large bowl using a hand mixer, cream the butter with the sea salt, powdered sugar and lavender until light and fluffy.
Step 2 Add the egg yolks, one at a time, beating well after each addition. Add the vanilla and beat until combined, about 10 seconds. Fold in the flour by hand, mixing lightly just until incorporated and being careful not to over-mix.
Step 3Remove the dough from the bowl and form it into a log 9 inches long and 2 inches thick. Wrap tightly in plastic wrap, and refrigerate for 2 hours, or until firm enough to slice.
Step 4Heat the oven to 350 degrees. Unwrap the log, and cut into one-fourth-inch slices. Place them on parchment-lined baking sheets, and bake for 8 to 10 minutes, until set (the cookies should not color).
Step 5Cool the cookies (still on the pans) on a rack. Then dust lightly with powdered sugar. They will keep for a few days in a container.