Preheat the oven to 325 degrees F.
Bring 2 quarts of water to a boil. Whisk together the cream and pistachio paste in a large saucepot, and then scrape and add the vanilla bean and the pistachios. Steep over medium-low heat 20 minutes, and then remove from the heat.
Whisk together 1 cup of the sugar and the egg yolks in a large bowl. Add 1/2 cup of the warm cream to the yolks and whisk quickly to temper the egg mixture. Add in the remaining cream, a little at a time, whisking constantly. When all of the cream has been incorporated, strain the custard through a fine mesh sieve into a large bowl.
Place 4 creme brulee ramekins into a 2-inch-deep baking pan. Evenly divide the custard between the ramekins, filling to the top. Carefully add the boiling water into the pan until it is halfway up the sides of the ramekins. Cover with aluminum foil.
Carefully (so no water gets in the custard) place the baking pan into the oven and bake until the custard is set, 25 to 30 minutes.
Remove the ramekins from the water bath and refrigerate.
Combine the blackberries, mint, pomegranate seeds and remaining 2 tablespoons sugar in a medium bowl, and let sit 10 minutes.
When the custards have cooled, sprinkle the tops with sugar and brulee with a torch until the sugar caramelizes. Garnish with the blackberry-pomegranate mixture and serve immediately.