Beat the butter until very smooth with an electric mixer.
While beating on medium-low speed, gradually add the sugar. When all the sugar is in, scrape the bowl and beater, add the lemon zest, and beat 2 to 3 minutes on medium speed until fluffy.
Beat the eggs and yolks with a fork to combine. On medium-low speed, dribble in the eggs and beat until very smooth, about 1 minute.
On low speed, gradually add the lemon juice (try not to splash) and the salt. The mixture will probably look a bit curdled. Don’t be alarmed; it will become smooth during cooking.
Scrape the sauce into a medium-to-large heavy-bottomed saucepan (3 to 4-quarts is a good size).
Set the pan over medium-low heat and stir constantly with a heatproof rubber spatula making sure to go all over the bottom, sides, and junctions of the pan. Remember, you’re cooking eggs, and if they overheat they’ll scramble. Just stir constantly and you’ll be fine. If you get nervous about cooking lemon curd over direct heat, set your saucepan into a larger pan (say, 12-inch skillet) with about an inch of barely simmering water.
As the curd heats it first thins out because the butter melts, then as the egg proteins unite, the curd transforms into a thick custard-like sauce. It takes about 10 minutes for the curd to thicken properly. If at any point you see the curd turning lumpy, immediately remove the pan from the heat and whisk the curd until smooth.The curd is close to being done when you see wisps of steam rising from its surface. It’s cooked when you swipe a finger on the curd-coated spatula and the path remains clear. The temperature on a digital thermometer will read 170˚F.
Scrape the curd into a bowl and press a piece of plastic wrap directly on its surface to keep a skin from forming. Refrigerate. It will thicken even more as it cools.
Lemon curd keeps well refrigerated for at least 1 week. It may also be frozen for up to 1 month.