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Set the butter out to come to room temperature.
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In a small bowl, whisk to combine flour, cornmeal, and sea salt.
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In the bowl of a stand mixer fitted with the paddle attachment or with hand held beaters, cream the butter and sugar until light and fluffy, about 2 minutes. Add the yolks one at a time, mixing until each is well combined. Add zest. With mixer on low, add the flour mixture and mix just until the dough starts to come together. Use a silicone spatula to fold any floury bits into the butter.
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Gather dough into a rough ball and press out on a sheet of plastic into a rough 6 x 10-inch rectangle. Chill dough for at least 30 minutes or as long as 3 days.
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When ready to bake, preheat oven to 300 degrees. Move baking rack to the center of the oven. Line 2 baking sheets with parchment.
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Set dough on a lightly floured surface. Give it a few minutes to soften slightly, and then roll it into a larger rectangle about ½-inch thick. Use a 2-inch cookie cutter to cut out your cookies. Arrange 12 - 15 on prepared baking sheet.
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Set baking sheet in the fridge to chill for 20 - 25 minutes.
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Gather up leftover dough, flatten into a rectangle, wrap in plastic, and set in the freezer for 10 minutes to re-chill. Then roll dough out, cut, and set cookies on the other baking sheet.
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When cutout cookies have chilled, slide into the oven and bake 10 minutes, rotate pan, and bake 7 - 10 minutes more, or just until the bottom edge of the cookies turns golden.
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Cool on baking sheet for 10 minutes, then remove to a wire rack to cool completely. Repeat process for the second batch of cookies.
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Once cookies are completely cool, make the icing by whisking to combine the powdered sugar, zest, and lemon juice. Dip each cookie in the icing, set on a wire rack, and decorate with thyme leaves and (if using) edible flowers. Allow icing to dry before serving or storing.
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Cookies will keep well in a sealed container at room temperature for 3 days.