Heat heavy cream in a saucepan over low heat until hot but not simmering.

Add sugar and chocolate to the hot cream and stir until melted and smooth.

Remove from heat and set aside.

In a bowl, beat egg yolks until thick.

Slowly pour the chocolate mixture into the beaten yolks, mixing well.

Stir in vanilla.

Preheat oven to 350F.

Strain the mixture into a shallow casserole dish.

Place the dish in a larger container and add boiling water halfway up the sides.

Bake for 40-45 minutes until lightly set.

Remove from water bath and cool for at least 1 hour.

Place the dish on an ice bath.

Sprinkle brown sugar evenly over the top.

Broil until the sugar melts and bubbles, watching carefully.

Cool and chill thoroughly before serving.