Put the blackberries and sprinkle with the vinegar. Let stand for 15 minutes. Reserve ½ cup of the berries for garnish. Divide the remaining berries among six standard-size flan dishes.
In a medium bowl, stir together the yogurt and sour cream and divide the mixture among the dishes. Drizzle with the honey. Refrigerate for 1 hour.
When ready to serve, place the dishes on a baking sheet and evenly sprinkle 1 tablespoon brown or turbinado sugar over each custard. Using a hand-held blowtorch, caramelize the sugar (see note below). Garnish the top of the caramelized sugar with the reserved blackberries.
