Make caramel: Set aside a 1 1/2- to 2-quart baking dish. In a small, heavy saucepan, bring 3/4 cup sugar and 3 Tbsp. water to a boil over medium-high heat, swirling pan until sugar dissolves, about 2 minutes. Let mixture boil undisturbed until caramel is a deep amber color, about 5 minutes. Immediately remove pan from heat and swirl to mix caramel. Pour into dish. Let cool.
Prepare custard: Preheat oven to 350°F. In a saucepan, scald milk and cream over medium heat. In a bowl, whisk together eggs, yolks and remaining 1/2 cup sugar for 1 minute. Gradually whisk in hot milk mixture and vanilla. Pour mixture through a strainer onto caramel.
Place dish inside a 13-by-9- inch baking dish. Pour hot water around custard dish to come halfway up sides. Bake until custard is set and golden on top, about 45 minutes. Remove dish from water bath and let cool for about 1 hour. Refrigerate until cold, about 3 hours.
To unmold, run a thin sharp knife around sides of loaf. Invert a platter on top of loaf and flip over to turn out custard.