Beat eggs and sugar at medium speed with an electric mixer until blended. Set aside.
Bring whipping cream to a boil in a medium saucepan over medium-high heat. Gradually add to egg mixture, beating at low speed until blended; stir in vanilla.
Pour into 8 (5- x 1-inch) round baking dishes.
Place baking dishes in a 15- x 10-inch pan.
Add hot water to depth of 1/2 inch.
Bake at 275 for 45 to 50 minutes or until almost set.
Remove custard cups from pan, and cool on a wire rack. Cover and chill at least 8 hours.
Sprinkle each custard with 1 tablespoon brown sugar, and place in a pan.
Broil 5 1/2 inches from heat (with electric oven door partially open) until sugar melts (about 2 to 3 minutes).
