For the candied lemon peels: Set a wire rack into a rimmed baking sheet. Use a vegetable peeler to peel 1/2-inch strips from 3 of the lemons; reserve. Juice all 5 lemons (you should have about 1/2 cup); cover and refrigerate the juice. Put the reserved strips of peel into a medium saucepan and cover with cold water. Bring the water to a boil, and cook for 10 minutes. Drain the peels and repeat the process 2 more times. Pat the peels completely dry.
Add 1/2 cup granulated sugar and 1/4 cup water to a medium saucepan and bring to a simmer over medium heat. Add the peels and cook until they start to turn translucent, 6 to 7 minutes. Use tongs to remove them from the saucepan and lie them flat on the prepared rack. Let dry at room temperature, 6 hours and up to overnight. Toss the peels with 1 tablespoon granulated sugar in a small bowl.
For the shortbread crust: Position an oven rack in the bottom third of the oven and preheat the oven to 350 degrees F. Spray a 9-inch tart pan with cooking spray.
Add the flour, butter and confectioners' sugar to a food processor. Pulse until the mixture resembles coarse meal with some pea-sized pieces. Add the egg and pulse until the dough comes together. Press the dough into the bottom and up the sides of the prepared tart pan. Prick the dough all over with a fork. Bake until the crust is golden brown, 20 to 25 minutes. Let cool slightly on a rack, about 30 minutes.
For the lemon curd: Meanwhile, whisk the reserved lemon juice, eggs, yolks, milk and remaining 1/2 cup granulated sugar in a medium saucepan over medium heat until well combined. Add the butter and stir continuously until the mixture is thick and coats the back of a spoon, 10 to 12 minutes. Strain the curd if any lumps form, then pour into the crust and smooth with a spatula.
Bake until the curd is set, 15 to 17 minutes. Let cool slightly on a rack, about 30 minutes, then transfer to the fridge to cool completely, about 1 hour more. Decorate with the candied peels and serve cold.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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