Let butter sit at room temperature until it is malleable but still cool, about 10 to 15 minutes.
Place confectioners' sugar in the bowl of an electric mixer fitted with the paddle attachment. Add butter, and toss to coat. Cream sugar and butter mixture on medium speed until the sugar is no longer visible. Scrape down the sides of the bowl. Add egg yolk, and beat until well blended. Scrape down the bowl. Add half the flour, and beat until the dough becomes crumbly. Stop the machine, and add the remaining 3/4 cup flour. Beat until the dough forms a sticky mass.
Remove dough from the bowl. Shape into a disk, and wrap in plastic. Refrigerate until firm, about 2 hours.
Dust work surface with flour. Remove chilled dough from refrigerator, and place on surface. Using the heel of your hand, knead the dough until it becomes malleable and slightly warm, about 1 minute. Knead the dough back into a smooth disk. As you work, use a dough scraper to free the dough from the surface. Keep the surface well dusted with flour. Roll the disk into a 12-inch log, and cut into 8 pieces. Refrigerate for 5 minutes.
Line a baking sheet with parchment or a silpat baking mat. Set 8 (4-inch) flan rings on baking sheet.
Dust work surface and rolling pin with flour. Using your fist, flatten 1 piece of dough into a 2- to 3-inch round. Lift up dough off work surface, and dust underneath with flour. Using a rolling pin, roll the dough into a 5 1/2-inch round, about 1/8-inch thick. With a pastry docker or fork, prick holes all over the dough. If the dough is too soft to handle at this point, use a dough scraper to move it to a small baking sheet, and refrigerate it for 2 to 3 minutes before proceeding.
Center the round of dough over the flan ring. With your thumbs on the inside and the tips of your fingers outside, run your hands around the ring several times, easing the dough down into it. Lower your thumbs to the inside bottom of the ring, and press to form a right angle between the bottom and sides of the dough. Keeping your thumbs on the inside of the ring, again circle around it, applying light pressure to the sides; if you move the ring around through your hands, the process will be easier. There should be at least a 1/2-inch rim of excess dough extending above the top edge. With a small knife, tilted upwards, trim the excess dough so it's flush with the top of the ring. Repeat this process with the remaining pieces of dough.
Place tart shells in the freezer to chill until firm, about 30 minutes.
Position rack in the center of the oven and heat the oven to 375 degrees F.
Bake until golden brown, 12 to 15 minutes. Remove from oven, and using a wide spatula, transfer shells to a wire rack to cool.
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