Preheat your oven to 425°F. Spray a 9-inch round tart pan with a removable bottom with non-stick cooking spray to ensure easy release after baking. Set the pan aside while you prepare the crust.
In a large mixing bowl, whisk together the all-purpose flour, unsweetened dark cocoa powder, white sugar, and 1/2 teaspoon kosher salt. Make a well in the center of the dry ingredients and pour in the melted unsalted butter. Stir everything together until the mixture forms a crumbly dough. I like to use my hands for the final mix to make sure the butter is evenly distributed.
Press the chocolate dough evenly into the bottom and up the sides of the prepared tart pan. Place the tart pan on a baking sheet to catch any drips and bake the crust in the preheated oven for 10 minutes. The crust may bubble slightly during baking. Remove the crust from the oven and let it cool for about 10 minutes while you prepare the filling.
In a clean mixing bowl, whisk together the pure pumpkin, sweetened condensed milk, large egg, pumpkin pie spice, and 1/4 teaspoon kosher salt until smooth and fully combined. This mixture will become the rich, spiced filling for your tart.
Pour the pumpkin filling into the cooled chocolate crust. Bake at 425°F for 10 minutes, then reduce the oven temperature to 350°F and continue baking for another 25-30 minutes, until the filling is set and a toothpick inserted in the center comes out clean. I always check a few minutes before the minimum baking time to avoid overbaking.
Let the tart cool in the pan for at least 1 hour before serving to allow the filling to set completely. For an extra touch, you can serve each slice with a dollop of whipped cream, if you like.