While the tart dough is chilling, in a medium bowl, whisk together egg yolks and 1/4 cup of granulated sugar. Whisk until the mixture turns a light yellow (about 30-45 seconds).
Add all-purpose flour, and cornstarch, and continue whisking until fully incorporated.
Next, slowly add only 1/4 cup of milk. Whisk until the mixture loosens slightly. This is your egg mixture. Set aside.
In a separate medium sized saucepan, combine the remainder 1 cup of milk, unsalted butter, and the remaining 2 tsp of sugar.
Scrape the seeds from the center of the vanilla pod, and add the vanilla seeds and pod to the saucepan. Heat the mixture over medium heat until it begins simmering. When the milk mixture begins simmering, turn off the heat.
Slowly pour the warm milk mixture into the egg mixture, while continuously mixing. Once all of the milk mixture is added to the egg mixture, return the entire mixture to the medium saucepan.
Warm the mixture over medium-high heat, while whisking continuously. While whisking, watch the mixture closely for signs of boiling. When the mixture begins to boil, continue stirring for about 30-45 seconds after this point.
Remove from heat. The mixture should be think and smooth like pudding.
Pour the mixture into a clean bowl and place a sheet of plastic wrap onto the surface of mixture. You want it to be in complete contact. Place the pastry cream in the refrigerator for at least one hour to cool.