Combine the 5 tablespoons butter, the powdered sugar, and salt in a food processor. 

Process until creamed together. 

To the creamed butter, add the egg yolks, the lemon zest, and the vanilla bean paste. Pulse until thoroughly combined.

Add the all-purpose flour and pulse until the mixture looks like coarse breadcrumbs. 

Sprinkle the cold milk over the flour and butter mixture. Pulse until the dough is just beginning to come together. 

Transfer to a work surface and gently work the dough together until you have a ball of dough. Try not to overwork the dough, as it will become tough. 

Shape the dough into a long cylinder and wrap in plastic wrap. 

Let the dough chill in the fridge for an hour or more. 

Cut the cylinder into slices and press the dough evenly into a 9” x 2” fluted tart pan or pan with removable bottom or even a cake pan. If you use a cake pan, you will have to carefully invert the finished chilled tart onto a plat and then invert the removed tart onto a serving platter. When pressing out the dough make sure it is as evenly as possible and all the way up to the top of the sides.

Freeze the tart pan with the dough for at least 1 hour or overnight.

In a 4 quart or larger saucepan, heat the whole milk and the vanilla bean or vanilla bean paste to barely a simmer. 

Take the pan off the heat and let steep for 10 minutes.

While the milk mixture is seeping, whisk together the sugar, the cornstarch and the salt in a large heatproof bowl.

Beat in the egg yolks and the whole eggs. Beat the mixture for 2 minutes until the mixture is thoroughly combined.

When the milk has seeped for 10 minutes, whisking constantly, add the egg mixture. 

Take this moment to clean out the mixing bowl as you will need it in a minute. Place a fine mesh strainer over the mixing bowl and set aside.

Heat the custard mixture over medium heat constantly whisking until the mixture starts to thicken, it may be a bit lumpy. It should resemble a thick pudding. 

Pour the hot custard mixture through the fine mesh strainer into the heatproof bowl. You may need to use a spatula to help press through the strainer. Discard the vanilla bean if using. (or rinse off the bean and place it into a jar of sugar to make vanilla sugar)

Press a piece of plastic wrap directly onto the surface of the cooked custard to prevent a skin forming. 

Let the mixture cool to room temperature, usually about 1 ½ hours. At this point, the mixture can be refrigerated overnight or used right away.

Preheat the oven to 375°. 

Spread the cooled custard into the frozen tart shell. Smooth out the top as evenly as possible.

Bake the tart for 55 – 65 minutes in the center of the oven until the tart just begins to brown on the top and the custard looks slightly jiggly in the center but firmer towards the edges.  

Turn the broiler on to high and broil for 5 minutes or so if the top isn’t nicely dark brown. Keep an eye on it as it will go to dark very quickly. It doesn’t have to be completely dark brown, but 50% of it should be.

Let the custard cool for 1 hour and then refrigerate for several hour or overnight.

Cut the tart into thick wedges and serve.