Place a fine-mesh sieve over a medium bowl; set aside. In another medium bowl, whisk together eggs and egg yolks until well combined; set aside.

In a medium saucepan, stir together sugar, lemon zest and juice, and salt. Cook over medium-low heat until sugar is dissolved and mixture begins to steam. (Do not boil.) Pour lemon mixture into egg mixture in a slow, steady stream, whisking constantly. Return mixture to saucepan. Cook, stirring slowly and constantly in a figure eight motion with a silicone spatula, until curd is thickened and can coat the back of a spoon and an instant-read thermometer registers 175°F (79°C) to 180°F (82°C), 10 to 12 minutes.

Press curd through prepared sieve into bowl, discarding solids. Add butter, 1 to 2 cubes at a time, stirring until melted each addition. Cover with a piece of plastic wrap, pressing wrap directly onto surface of curd to prevent a skin from forming. Refrigerate until well chilled and set, at least 2 hours. Store in an airtight container in refrigerator for up to 2 weeks.