Preheat the oven to 325 degrees F. Bring the cream to a simmer in a medium saucepan over medium heat. Remove from the heat.
Whisk together the egg yolks and granulated sugar in a medium bowl until they are pale yellow and thickened. Whisk the warm cream into the egg mixture, a small amount at a time. Add the vanilla extract and whisk until mixed in. Pour the custard into six 8-ounce custard dishes.
Put the custard dishes in a deep baking dish lined with a tea towel. Pour in boiling water so that it comes halfway up the sides of the custard dishes. Bake until the custard is firm but still wiggles, about 40 minutes. Remove from the water bath and refrigerate until firm, about 1 hour
Preheat the broiler. Top each custard with an even layer of turbinado sugar and broil until the sugar melts and bubbles.