Preheat oven to 350°F. Whisk the flour and salt together in a small bowl. Set aside.
In a medium bowl, cream together the butter and sugar until smooth, about 2 minutes. Add half of the flour mixture, and then repeat with the remaining flour mixture. The dough will be crumbly, but should form together when you pinch it.
Spoon the dough a 9-10 inch tart pan, and press it with your fingers until evenly distributed. Poke the dough all over with the tines of a fork. Bake until lightly golden brown, about 20-22 minutes.
When the tart is finished baking, let it cool for 15-20 minutes. Lower the temperature of the oven to 300°F.
Whisk egg yolks and sugar in a medium bowl until thick and pale yellow, about 3 minutes.
In a small saucepan, combine the heavy whipping cream, cinnamon, and pumpkin pie spice. Heat over medium, and let the mixture simmer for two minutes.
Slowly add about one-third cup of the cream mixture to the egg mixture, whisking vigorously to avoid scrambling the eggs. Once tempered, slowly whisk in the remaining cream mixture until frothy. Add the vanilla extract and pumpkin purée.
Make sure your oven is set to 300°F! Place the tart pan on a four-sided sheet pan, and put it on the middle rack of your oven. Pour the custard mixture into the tart pan. Bake until just set but a little wobbly in the center, about 30-35 minutes (it will continue setting as it cools).
Let the tart cool at room-temperature for 30 minutes. Then, let it finish setting in the fridge for at least two hours.
Right before serving, sprinkle the crème brûlée with 2 tablespoons of sugar. Torch the sugar until it is melted and caramelized. Repeat the process with the remaining 2 tablespoons of sugar. Slice and serve immediately.
If you do not have a torch, caramelize the sugar under a broiler in the oven, watching it very carefully and pulling it out right when the sugar melts. Cover the edges of the tart shell with tinfoil if it starts to get too browned.