Preheat oven to 325 degrees F. In a small heavy saucepan cook and stir 1/2 cup of the half-and-half and the white chocolate over low heat just until chocolate is melted. Gradually whisk in the remaining 1 1/4 cups half-and-half. Bring to simmering. Remove from heat.
Meanwhile, in a medium bowl whisk together egg yolks, 1/3 cup sugar, vanilla, and salt just until combined. Slowly whisk hot chocolate mixture into egg mixture.
Place six 4-ounce ramekins or 6-ounce custard cups in a 3-quart rectangular baking dish. Divide egg mixture evenly among ramekins. Place baking dish on oven rack. Pour enough boiling water into baking dish to reach halfway up sides of ramekins.
Bake for 30 to 40 minutes or until a knife inserted near the centers comes out clean (centers will shake slightly). Remove ramekins from water; cool on a wire rack. Cover and chill for 1 to 8 hours.
Before serving, let custards stand at room temperature for 20 minutes. Meanwhile, for caramelized sugar, in an 8-inch heavy skillet heat 2 tablespoons sugar over medium-high heat until sugar begins to melt, shaking skillet occasionally to heat sugar evenly. Do not stir. Once the sugar starts to melt, reduce heat to low and cook about 3 minutes or until all of the sugar is melted and golden, stirring as needed with a wooden spoon.
Quickly drizzle caramelized sugar over custards. (If sugar hardens in the skillet, return to heat; stir until melted.) Serve immediately.