For the tart crust: To the basin of a food processor, add flour, sugar, and salt. Briefly pulse to combine.
Add butter and pulse until coarse crumbs form (about ten 1-second pulses).
In a separate, small dish, whisk together egg and vanilla. Drizzle over flour mixture, and pulse until dough just begins to cling together.
Carefully remove from food processor (watch the blade) and shape dough into a disc, wrap in plastic wrap, and chill for 1 hour.
Roll chilled dough into a 10-11″ (25cm) disc and press into a 9″ (23cm) tart pan. Prick the bottom all over with a fork, line with parchment paper, and fill with pie weights or dry beans. Freeze for 30 minutes, meanwhile preheat oven to 375°F (190°C).
Once crust has chilled and oven is preheated, bake crust in center rack of 375°F (190°C) oven for 20 minutes or until edges are light golden brown. Remove parchment and weights (carefully), then bake for an additional 5 minutes (the bottom of the tart should be beginning to turn lightly golden). Prepare lemon filling.
Lemon Filling: In a medium-sized, stainless steel saucepan (see note), combine eggs, egg yolks, lemon juice, sugar, and salt. Add butter and cook over medium-low heat, stirring constantly, until mixture is thickened and coats the back of a spoon.
Remove from heat and pour mixture through a fine mesh strainer into a bowl, then pour into tart crust and spread evenly. Cool at room temperature for 1 hour, then refrigerate for at least 6 hours or overnight.
Whipped Cream (optional): Combine heavy cream, powdered sugar, and vanilla extract. Beat on high speed until stiff peaks form. Pipe or dollop whipped cream onto tart before serving. I used an Ateco 848 to add the decorative whipped cream on top.