Set the oven to 350°F and arrange an oven rack in the center position.
Add the graham crackers to a food processor and pulse until they are reduced to fine, even crumbs.
Place the light brown sugar, fine sea salt, and melted butter into the processor with the crumbs. Process again until everything is evenly incorporated and the mixture has the consistency of damp sand.
Transfer the crumb mixture to a tart pan. Distribute it evenly across the base and along the sides.
Press the crumbs down firmly over the bottom and against the sides, forming a tightly packed shell with a rim approximately 1/4 inch thick.
Bake for about 10 minutes, or until the crust becomes golden and aromatic.
Remove the tart shell from the oven and allow it to cool completely on a wire rack.
The baked crust may also be prepared one day in advance and kept tightly covered with plastic wrap at room temperature.
Combine the milk or half-and-half, 1/3 cup granulated sugar, kosher salt, and the scraped vanilla seeds and pod in a medium saucepan.
Warm over medium-high heat until the mixture just reaches a simmer. Do not allow it to come to a full boil.
When using a vanilla bean, remove the saucepan from the heat and leave the mixture undisturbed for 15 minutes so the vanilla can infuse into the milk.
When using vanilla extract instead, omit the 15-minute infusion period and reserve the extract for incorporation later.
While the vanilla milk is infusing, place the egg yolks, cornstarch, and remaining 1/4 cup granulated sugar in a medium bowl.
Whisk thoroughly until the ingredients are completely blended and the mixture has thickened slightly.
If a vanilla bean was used, remove and discard the pod. Return the infused milk mixture to the heat and bring it back to a gentle simmer.
While whisking continuously, gradually pour approximately half of the hot milk into the egg yolk mixture. Adding the milk slowly tempers the yolks without scrambling them.
Pour the warmed egg mixture back into the saucepan containing the remaining milk, continuing to whisk as you combine them.
Reduce the heat to low and cook the custard while stirring steadily with a wooden spoon. Continue for approximately 5 to 7 minutes, or until the mixture noticeably thickens.
Should the custard begin to appear curdled or uneven, change to a whisk and beat it vigorously until smoother.
Continue cooking and whisking constantly for an additional 2 minutes. The finished pastry cream should be very thick, with a pudding-like consistency.
Remove the saucepan from the heat. Immediately whisk in the 4 tablespoons of unsalted butter. If vanilla extract is being used in place of the vanilla bean, whisk in the 2 1/2 teaspoons of extract at this stage.
If any lumps remain, pass the warm pastry cream through a fine-mesh sieve.
Press plastic wrap directly against the surface of the custard to prevent a skin from developing. Refrigerate for at least 3 hours, or for as long as 2 days, until completely cold and firmly set.
Once thoroughly chilled, measure 3 cups of the cold pastry cream. Using a hand whisk or a stand mixer fitted with the paddle attachment, mix the custard for approximately 1 to 2 minutes, until it becomes smooth and lighter in texture.
Spoon or pour the loosened pastry cream into the completely cooled graham cracker crust. Spread the filling evenly and smooth the surface.
The assembled tart may be refrigerated for up to one day before serving. For the freshest appearance and texture, wait until shortly before serving to add the fruit and decorative garnishes.
Arrange fresh berries over the custard and add mint sprigs as desired. For a polished, glossy finish, lightly brush the berries with jam that has been thinned with a little hot water.