Set a fine-mesh sieve over a clean bowl and keep it nearby. Cut the butter into 5–6 pieces and let it soften slightly. If you want to chill the curd quickly, prepare an ice bath (a larger bowl filled with ice and water) to nest the finished bowl later.
In a small saucepan, combine the lemon juice, lemon zest, and a pinch of salt. Warm over low heat just until steaming and fragrant (do not boil), then remove from heat, cover, and let the zest infuse for 5 minutes.
In a separate heavy-bottomed saucepan off the heat, whisk together the sugar, the 2 whole eggs, and the additional yolk until the mixture is smooth and slightly lightened, about 30 seconds.
Temper the eggs: slowly pour the warm lemon mixture through the sieve into the egg-sugar mixture while whisking constantly (this catches the zest now and prevents curdling). Discard the strained zest.
Cook over low to medium-low heat, stirring steadily with a heatproof spatula and occasionally whisking, until the curd thickens enough to coat the back of a spoon and reaches 170–175°F, about 7–10 minutes. Avoid boiling.
Remove from the heat and add the butter pieces, stirring until fully melted and glossy. Whisk in the vanilla, if using. For extra-silky texture, blend briefly with an immersion blender (15–30 seconds).
Press the hot curd once more through the prepared sieve into a shallow dish or jar to ensure perfect smoothness. Press plastic wrap directly onto the surface to prevent a skin.
Cool over the ice bath for 10 minutes if using, then refrigerate until set and chilled, at least 2 hours. Stir before serving.