In a medium bowl, whisk egg yolks with 1/3 cup sugar until smooth.
In a medium saucepan, bring the cream to a simmer over medium-high heat. Add the white chocolate. Turn off the heat and whisk until the white chocolate is melted. Add 2 tablespoons of the white chocolate mixture to the egg yolk mixture, whisking continually to prevent the eggs from scrambling. Add the remaining white chocolate mixture to the egg yolk mixture. Whisk until smooth. Add the vanilla.
Pour into four 6-inch ramekins or custard cups. Place the cups in a 9 by 13-inch baking pan. Add enough hot water so the cups sit in 1 to 1 1/2 inches of water.
Bake for about 45 minutes, until set. Allow to cool, then refrigerate the custards until chilled. Before serving, sprinkle the tops of each ramekin with 1 teaspoon of sugar and place under the broiler until caramelized, 3 to 4 minutes. Rechill in refrigerator for 5 minutes before serving.