Whisk together whole eggs, yolks, and sugar in a metal bowl until combined well, 1 to 2 minutes. Set bowl over a saucepan of simmering water and whisk until foamy, about 2 minutes. Add one third of lemon juice and whisk until thickened, about 1 minute. Add half of remaining lemon juice and whisk until thickened, about 1 minute. Repeat with remaining lemon juice. Continue cooking, whisking constantly, until thickened and an instant-read thermometer registers 170°F, 7 to 8 minutes more. Remove from heat and whisk in butter, 1 piece at a time, until incorporated. Cool slightly.