Preheat oven to 325 degrees F. Butter a 9 by 12 1/2-inch baking sheet pan, line with parchment paper, and butter the paper.
Finely grate the skin (zest) off all 3 clementines, making sure you peel only the orange skin and not the bitter white pith. Puree the zest with 1/4 cup of the sugar in a food processor until minced, about 1 to 2 minutes.
Whisk the flour, cornstarch, and salt in a bowl. In a standing mixer fitted with the paddle attachment, cream the butter with the remaining 1/2 cup sugar on medium, until light and fluffy, about 8 minutes. Add the clementine-sugar mixture and beat for another minute. While mixing on low speed, add the dry ingredients and mix just until combined. Do not overwork the dough. Transfer dough to prepared pan, spreading it out as evenly as possible. Cover with plastic wrap, then press and flatten using your hands over the top to smooth and even out the dough. Cut the dough into bars about 1 by 3 inches with a sharp knife, while still in the pan. Prick a decorative pattern in the shortbreads with a fork or a wooden skewer. Bake until golden, about 1 hour and 10 to 20 minutes. Let stand for 5 minutes and then re-cut the bars along the previous cuts. Let cool completely on racks. Store the cookies in a sealed container for up to 2 weeks.
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