Place the butter, powdered sugar, and egg yolks in the bowl of a food processor fitted with the blade.

Pulse until combined but still speckled with butter.

Add the flour and run the machine just until the dough comes together when you pinch it between your fingers.

Turn dough out onto a large piece of parchment, knead a few times to bring it all together, and pat it into a disc shape.

Wrap well in the parchment and chill for about half an hour.

Preheat the oven to 350°F with a rack in the center.

Remove dough from the fridge and let it rest on the counter for 15 minutes.

Sprinkle a bit of flour on your work surface and over the surface of the dough. Roll out the dough with a rolling pin to an approximately 12-inch circle.

Transfer the dough very carefully to a 9-inch tart pan with a removable bottom, pressing on the dough lightly so it sits snugly against the bottom and sides of the pan. Prick the bottom of the shell all over with a fork. Place the whole thing onto a baking sheet.

Place a piece of parchment paper over the shell, making sure to cover the edges. Spread plenty of dried beans or pie weights over the parchment, covering the whole bottom of the tart shell.

Bake for 15 minutes this way, then remove the parchment and beans.

If you would like to egg wash the tart, beat the egg and water together with a fork in a small bowl. Brush the shell with a bit of the egg wash. (You'll have a lot left over and can use it to make scrambled eggs if you like.)

Return shell to the oven for an additional 15 minutes, until completely cooked through. If edges start to color too much, you can cover them lightly with foil.

Remove from the oven and cool completely before filling.

Fill a large bowl with a few inches of ice water and set a smaller bowl inside it, ensuring that the ice water won’t breach the sides. You’ll use this ice bath later to cool the custard.

Pour 2 ½ cups of the milk into a medium pot and the remaining ½ cup into a medium mixing bowl.

To the pot, add the sugar, salt, and vanilla bean. Set over medium heat and bring to a simmer, stirring occasionally to ensure sugar dissolves.

To the bowl, add the cornstarch, flour, and egg yolks. Whisk until smooth.

Slowly pour about one cup of the warm milk into the yolk mixture, whisking constantly.

Set a fine-mesh strainer over the pot and pour the contents of the bowl through it.

Set pot back on stovetop and bring contents to a boil, whisking constantly. When the mixture thickens and large bubbles begin to form and pop, continue cooking, whisking constantly, for one minute. Then remove from heat and immediately proceed to the next step.

Pour custard back through the strainer into the bowl set in the ice bath.

Stir in the butter.

Cover with plastic wrap or buttered parchment, making sure it touches the surface of the custard to prevent a skin from forming. Refrigerate until very cold. 

Spread custard gently and evenly into tart shell.

Shortly before serving, core strawberries and slice in half or into thin vertical slices, as you wish.

Arrange over custard.

Place jam and water into a small bowl, microwave until warm, and stir together until smooth. Strain through a fine-mesh sieve.

Brush evenly over strawberries.