Place blackberries in a medium saucepan over medium-high heat. Using a potato masher or a fork, crush the berries. Bring the berries to a simmer, then lower temperature to medium-low and simmer for about 5 minutes.
Remove pan from heat and pour berries into a fine-mesh strainer set over a glass measuring cup. Using the back of a ladle or spoon, press on the berries to squeeze out as much juice as possible. Discard seeds and solids.* Allow to cool completely.
Preheat the oven to 300ºF. Lay a kitchen towel along the bottom of a large baking pan or roasting pan. Place six 4-5 ounce ramekins on top of the towel; set aside.
In a large bowl, whisk the egg yolks, the 1/2 cup of sugar, cooled blackberry juice, vanilla, and salt together until smooth and combined. Gradually whisk in the cream until mixture is smooth and incorporated. Pour mixture through a fine mesh sieve to get out any lumps that might have formed.
Divide custard evenly among the six ramekins, then set the pan on the oven rack. Carefully pour enough hot water into the pan to come about halfway up the sides of the ramekins. Bake until custards are set around the edges and jiggle slightly in the center, about 40-50 minutes.**
Transfer ramekins to a wire rack and allow to cool to room temperature, about 2 hours. Place ramekins in a baking pan, cover tightly with plastic wrap, and refrigerate for at least 4 hours, preferably overnight.
Just before serving, sprinkle about 1 teaspoon of granulated sugar evenly over the entire surface of each custard. Use a kitchen torch to caramelize the tops. Enjoy!