1. In a medium saucepan, combine the heavy cream and 3 tablespoons sugar. Bring the mixture to a boil over medium heat. Remove the pan from the heat.
2. In a medium bowl, whisk together the egg yolks and another 3 tablespoons sugar. Gradually pour the egg mixture into the saucepan, whisking constantly. Return the saucepan to the stove and cook on low heat for 3 minutes or until the mixture thickens. Add vanilla.
3. Layer the bottom of the cup with 2-3 tablespoons of the prepared sweet potatoes.
4. Fill the custard cups with enough of the cream mixture so they are about seven-eighths full. Place the filled cups in a baking pan that is large enough to hold them all. Add enough hot water to come within 1 inch of the top of the cups. Bake for 45 minutes, or until the custards are barely set and a toothpick inserted in the center comes out a little wet. Remove the custards from the baking pan and place them in the refrigerator. Refrigerate overnight.
5. Preheat the broiler. Lightly sprinkle the surface of each custard with 1-1/2 tablespoons of brown sugar. Place the custards under the broiler for 30 seconds and let them brown. Keep an eye on the custards, as this happens quickly. (Sugar can also be caramelized with a torch.)
6. Remove the custards from the heat, and once the sugar has hardened, serve.