Pumpkin Purée: Preheat the oven to 350F.
Line a baking sheet with silicone mat or parchment paper.
Cut off the top of squash to remove the stem. Cut into large wedges and using a spoon, remove the seeds. Place on baking sheet and bake for 35-45 minutes, or until soft when poked with a fork.
Remove from the oven and allow to cool. Once cooled, remove the skin and place in a blender and blend until smooth(you can also use an immersion blender). Pass puree through a sieve into a medium bowl. Set aside.
Make the shortcrust pastry: Add butter into the bowl of a stand mixer fitted with the paddle attachment. On low speed, beat until soft and creamy, about 2 minutes.
Add the confectioners’ sugar and vanilla. Beat until smooth, another minute.
Combine the egg and salt and add to the mixture. Scrape down the sides and beat for 30 seconds, or until incorporated. Add the flour and mix on low speed just until combined, about 30 seconds.
Add the flour and mix on low speed just until combined, about 30 seconds. Remove the dough from the bowl and shape into a flat disk. Wrap the dough in plastic wrap and refrigerate for 30 minutes.
Take the dough out of the fridge. Lightly flour a working surface the dough (and your rolling pin). Roll the dough into a rough circle until the pastry is rather thin, about 0.15–0.2 inches (0.4mm–0.5mm) thick. Occasionally, lift the dough up to prevent from sticking. Lightly flour the surface as needed. If the dough is tearing or getting too warm, place it back in the fridge for another 5-10 minutes.
Drape the dough over the tart pan. You can use a rolling pin for this and a bench scraper to help lift up the dough circle.
Using your fingers, press the dough into the edges of the fluted indents. If the dough is tearing, take any excess pastry and patch the holes as necessary. Using a sharp knife, remove the excess dough from the edges. You can also use your rolling pin by pressing it firmly against the top of the pan, then rolling it over the entire pan.
Place the tart pan on a baking sheet. Place it into the freezer for 30 minutes. Cut a large circle of parchment paper and scrunch it up until flexible, and set aside.
Remove the baking sheet from the freezer. Gently press the scrunched up paper into the edges of the pastry shell, making sure to cover the edges and completely line the tart. Pour baking beans or rice into the base and spread them out. Bake for 25 minutes.
Remove the baking sheet from the oven and carefully lift out the parchment paper with the baking beans on. Return the baking sheet to the oven and continue to bake the pastry until golden color, 5-10 minutes.
Remove from the oven and allow to cool for 10 minutes. Lightly brush the egg wash the inside of the tart shell. Place it back into the oven for 5-7 minutes, or until the egg wash has completely set and the pastry is golden.
Remove the tart shell from the oven and allow it to cool.
Make the filling: In a medium saucepan, whisk together the pumpkin puree, heavy cream, milk, sugar, cinnamon, nutmeg, allspice, ginger, and salt. Bring to a gentle simmer. Place egg yolks in a medium heat safe bowl. Remove pumpkin mixture from heat immediately.
Temper the egg yolks: pour in a small amount of the hot pumpkin mixture until into the egg yolks and whisk until well incorporated. Slowly add the remaining pumpkin mixture and gently mix until shiny and smooth – you don't want to incorporate air into the mix, so use a rubber spatula or an immersion blender for this part.
Pour the custard through the sieve into a bowl. Set aside.
Bake the tart: Place the tart shell on a baking sheet. Pour the custard into the tart shell. Bake for 20-25 minutes or until the custard is slightly wobbly in the center. Remove from the oven and allow to cool.
Make the meringue: Place the egg whites and sugar in the mixing bowl of your stand mixer or a large metal mixing bowl. Set it over a pan of simmering water. Stir continuously and vigorously so the egg whites do not cook. Check that the mixture is done cooking by rubbing some of it between your fingers and feeling if the sugar has fully dissolved. Once fully dissolved, turn off the heat and remove the bowl from the pot.
The mixture is done cooking when you rub some of it between your fingers and can feel the sugar has fully dissolved. Once fully dissolved, turn off the heat and remove the bowl from the pot.
Transfer the bowl to the stand mixer and whisk at high speed until stiff peaks form.
Assemble: Remove the tart from the pan and place the tart on a serving dish. Spoon the meringue on top of the custard filling and spread it out with the back of a spoon. Using a kitchen torch, toast the top of the meringue just before serving (you can also place it under your oven broiler).