Preheat the oven to 300°F (150°C).
Pat crab meat dry with paper towels, careful not to break up lumps.
Whisk together heavy cream and egg yolks until smooth.
Add shallot, chives, Dijon mustard, cayenne, salt, and pepper to the cream mixture, and stir gently to combine.
Fold in crab meat carefully, maintaining the lumps.
Divide the mixture into 4 shallow ramekins, place ramekins in a baking dish, and fill the dish with hot water halfway up the sides of the ramekins.
Bake for 20-25 minutes until just set but still slightly jiggly in the center.
Remove from water bath and cool for 5 minutes.
Sprinkle sugar evenly over each ramekin and caramelize the sugar with a kitchen torch until golden brown.
Let the sugar harden for 1 minute before serving.
Garnish with fresh herbs if desired.