1. Pour 2 cups water into a heavy saucepan. Add 1 cup of the sugar and bring to a boil.
2. Slice 1 of the lemons into thin circles, drop them into the water and sugar, lower the heat, and simmer for about 30 minutes, uncovered. Drain and discard the liquid.
3. Grate the zest of the remaining 3 lemons to get 2 tablespoons of zest, then squeeze the lemons to get about ¾ cup of juice.
4. Whip the eggs and remaining sugar in the bowl of a heavy-duty mixer at medium speed. Gradually add the lemon juice and zest.
6. Pour into a medium saucepan, add the butter, and cook over medium heat, stirring constantly, being careful not to boil, until the lemon thickens into a curdlike custard, about 5 minutes.
Pie Crust
1 cup all-purpose flour
¼ teaspoon salt
2 tablespoons sugar
½ cup (1 stick) unsalted butter
1½ tablespoons ice water
1. Mix the flour, salt, and sugar together in the bowl of a food processor. Then cut the butter in small pieces, drop them through the tube of the food processor, and pulse long enough to say "alligator" 10 times. Pour in the ice water and pulse again, saying "alligator" 8 times. Transfer the dough to a marble countertop or work surface and smear it out with the heel of your hand in small increments, then gather the dough together in a round. You can also use your fingertips to mix the flour, salt, sugar, and butter by band to the consistency of cornmeal. Then drizzle on the water and work it into the dough before smearing it out with the heel of your hand. Cover with plastic wrap and refrigerate at least 15 minutes or until ready to use.
2. Preheat the oven to 425 degrees.
3. Sprinkle some flour on the marble or a countertop and on a rolling pin. Roll out the dough to an approximately 11-inch cirle, then press it into an 8-inch tart pan with a removable bottom. Do not worry if the dough cracks a bit—just press it together.
4. Line the crust with aluminum foil and fill with small weights, such as dried beans, rice, or pebbles. Bake for 15 minutes, then remove the foil and weights, reduce the oven to 350 degrees, and bake for another 10 minutes. Remove the crust from the oven and let it cool slightly.
