Using a stand mixer fitted with the paddle attachment (or a large mixing bowl with a hand mixer), combine the butter, sugar, eggs and egg yolks and beat on medium-high speed for 2 minutes. Add the lemon juice and zest and beat until just combined.
Add the mixture to a medium saucepan and cook over medium-low heat until smooth. Increase to medium heat and cook, stirring constantly, until the mixture is thick and yellow in color, about 10 minutes.
Remove from the heat and let cool. Pour into a bowl and press plastic wrap directly on surface to prevent skin from forming. Chill in refrigerator for up to 3 days.
Notes
When whisking the mixture on the stove top, be sure to WHISK CONSTANTLY and briskly to avoid the eggs turning into scrambled eggs.
Press plastic wrap directly onto the surface when chilling to prevent skin from forming.