Prepare: Place a fine mesh sieve over a medium-size glass bowl then set aside.
Whisk: Add whole eggs plus egg yolks to another medium-size glass bowl then vigorously whisk until smooth.
Heat: To a medium-size, heavy-bottom saucepan add the lemon juice, sugar, and salt. Turn the heat to medium then whisk to combine the ingredients. Cook while slowly whisking until the sugar has dissolved, 2-3 minutes.
Temper: Remove the pan from the heat then slowly stream ~3/4 cup of the hot lemon-sugar mixture into the bowl with the eggs while whisking vigorously.
Cook: Slowly stream the tempered eggs into the saucepan with the remaining lemon-sugar mixture while whisking vigorously. Place the pan over medium-low heat then whisk continuously until the mixture has thickened, 4-5 minutes.
Strain: Scrape the lemon curd into the fine mesh sieve over the glass bowl with a spatula then press it through.
Cool: Add half the cold butter then stir until melted. Add the remaining butter then stir until melted. Add the vanilla extract then stir until combined. Place a piece of saran wrap directly on top of the lemon curd then refrigerate until completely chilled before using, 2-3 hours.
Store: Lemon Curd can be refrigerated for up to 2 weeks, or frozen for up to 3 months.