Preheat oven to 325°F (163°C) and arrange six ramekins in a baking dish.
Warm heavy cream, Dijon mustard, Old Bay seasoning, cayenne pepper, salt, and pepper in a saucepan without boiling.
Beat egg yolks in a bowl and temper by slowly whisking in the hot cream mixture.
Stir in fresh lump crab meat evenly into the custard.
Divide the custard mixture evenly among the ramekins.
Prepare a water bath by adding hot water halfway up the sides of the ramekins.
Bake for 35-40 minutes until custard is set but slightly jiggly in the center.
Cool to room temperature, then refrigerate for at least 2 hours or overnight.
Before serving, sprinkle sugar on top and caramelize using a kitchen torch.
Garnish with fresh chives and serve immediately.