Crust
Whisk sugar, salt, and 2⅔ cups flour in a large bowl. Add butter and, using your fingers, smash each piece into a thin disk. Take your time doing this and don’t feel compelled to break butter into even smaller pieces. Drizzle ⅔ cup ice water over, dispersing it as widely as possible, and mix with a rubber spatula to bring mixture together into a shaggy mass.
Turn dough out onto a surface and work together with your hands, pushing and flattening until dough holds together when squeezed in your palm but some streaks of dry flour are still visible. Divide dough into 2 portions.
Flatten 1 portion of dough into an 8 inch diameter disk. Cut into quarters, stack pieces on top of one another, and flatten dough with a rolling pin to about half of its original height. At this point dough should hold together with no dry spots remaining, and have nice big flakes of butter showing. Use a bench scraper or a large knife to clean any clingy bits of dough from surface. Dust surface with flour, then dust top of dough with flour. Roll out to a ¼–⅜ inch thick round. Wrap dough around rolling pin and transfer to a standard 9 inch diameter pie dish. Unfurl into dish, then lift edges and allow dough to slump down into dish. Trim overhang to an even 1 inch (there will be some excess). Fold overhang under and crimp as desired. Cover and chill until very cold, at least 1 hour and up to 12 hours (cover tightly if chilling longer than 1 hour). Repeat process with remaining dough and another pie dish. Or form into a 1½ inch thick disk, wrap in plastic, and chill up to 3 days (or freeze up to 1 month).
Place a rack in middle of oven; preheat oven to 400°. Lay 2 sheets of parchment paper over dough and fill with pie weights or dried beans (they should fill the dish). Set on a foil-lined rimmed baking sheet (this will keep any butter drips from smoking up your oven). Bake until edges are golden brown and bottom is opaque (carefully lift parchment to check), 30–35 minutes. Remove from oven; reduce oven temperature to 300°. Lift out parchment and weights. Bake crust until evenly chestnut brown all over, 10–15 minutes. If baking both crusts, turn oven dial back up to 400° and let oven preheat; repeat with remaining crust.
Filling
Whisk sugar and cornstarch in a large saucepan to combine. Add eggs and egg yolks and whisk vigorously, making sure to get into corners of pan, until smooth and pale. Whisk in lemon zest and juice, salt, and 1½ cups water.
Place saucepan over medium heat and bring to a simmer, whisking often and making sure to get into corners of pan, 8–10 minutes (mixture should be bubbling and thickened). Reduce heat and continue to simmer, whisking constantly, 3 minutes. Let cool 5 minutes, whisking every minute.
Add butter to filling and whisk until melted and fully incorporated. Scrape filling into pie crust; smooth surface. Chill until cold and set, at least 2 hours and up to 3 days.
Assembly
Combine egg whites, sugar, salt, and cream of tartar in the bowl of a stand mixer or another large heatproof bowl; set over a large saucepan filled with 1 inch simmering water (bowl shouldn’t touch the water). Heat, stirring constantly, until sugar is dissolved and mixture is warm to the touch, about 4 minutes.
Fit bowl onto mixer fitted with whisk attachment (or use an electric mixer) and beat on medium-high speed until meringue is more than tripled in volume and medium peaks form, about 4 minutes. Transfer to a piping bag fitted with a large round tip (or a resealable plastic bag will work—just snip off a corner after bag is filled). Pipe meringue over filling and toast with a kitchen torch or under the broiler.
Do Ahead
Pie (without meringue) can be made 2 days ahead. Keep chilled.