For the Tart Dough
In a mixing bowl, add the sugar. Then slowly add 2 pieces of cold butter cubes at a time. Continue to add butter until the mixture is smooth - about 5 minutes. Add the egg and vanilla extract. Make sure you scrape the mixing bowl to combine all of the ingredients well.
In a separate bowl, whisk together the dry ingredients. Slowly add the dry ingredients into the mixing bowl until the dough comes together and is smooth. Do not overmix the dough!
Wrap the dough in plastic or put it in a container and let it chill in the refrigerator for one hour.
Lightly grease a 9-inch tart pan (preferably with a removable bottom). Remove the dough from the refrigerator and let it sit for 1-2 minutes to soften slightly. If the dough is too soft, it will be difficult to work with. You want the dough cold.
On a floured surface (I recommend a Silpat, see notes below), roll the tart dough into an 11-inch circle and 1/8 – 1/4 inch thickness. Quickly take the dough and place it inside a 9-inch tart pan. To do this efficiently, flour the dough and rolling pin. Roll the dough loosely around it, then unroll it into the tart pan. If the dough is too warm and soft, place it in the refrigerator for 5 minutes to get cold again. (See notes for great tips below).
Using your fingers, gently form the dough into the pan. With a sharp knife, trim the edges of dough that are above the tart pan. Place the tart shell in the refrigerator for about 30 minutes or until it is chilled. While the dough is chilling, preheat the oven to 375°F.
Remove the chilled tart shell. Dock the bottom of the tart with a fork. Line the tart with parchment paper larger than the pan. Additionally, cover the edges of the pan with aluminum foil to prevent from burning. Fill the tart pan with weights such as baking beans, dried beans, or uncooked rice. Make sure they are fully distributed over the entire surface for even baking.
Bake the tart at 375°F for 12 minutes. Remove the parchment paper with the weight (leave the foil on the edges) and bake for an additional 10 minutes or until the tart shell is fully baked. Once the shell is baked, remove from the oven and let it cool completely.
For the Lemon Curd
In a large bowl, whisk together the eggs and egg yolks.
In a large saucepan, bring the sugar and lemon juice to a boil. Remove the saucepan from the heat and temper the eggs by slowly adding the hot liquid into the bowl while whisking. Keep pouring the liquid into the eggs while mixing everything together to prevent the eggs from curdling. Once everything is mixed together in the bowl, pour the ingredients back into the large saucepan.
Turn the heat on medium and constantly whisk the lemon curd until it thickens. You should cook the lemon curd for at least 3 - 5 minutes or until it coats the back of a wooden spoon.
While whisking, add a few pieces of the cubed butter at a time into the lemon curd. Once all of the butter is fully melted and incorporated, remove the saucepan from the heat.
Strain the lemon curd through a sieve. Slightly cool the lemon curd and then pour it into the baked sweet tart dough. Lightly tap the tart shell to remove any bubbles and create a smooth surface. Let the classic French lemon tart set in the refrigerator for at least 4 hours.
You can serve the lemon tart plain, decorate with fresh berries, write "citron" in chocolate, or even top with meringue. Enjoy!