for the Bread Pudding
2 tablespoons light brown sugar
3/4 cup plus 1 tablespoon granulated sugar
1 loaf challah bread, cut into 3/4-inch cubes (about 10 cups)
9 large egg yolks
4 teaspoons vanilla extract
3/4 teaspoon table salt
2 1/2 cups heavy cream
2 1/2 cups milk
2 tablespoons unsalted butter, melted
for the Sauce
1 cup (packed) dark brown sugar
1/2 cup whipping cream
6 tablespoons (3/4 stick) unsalted butter
1/4 cup light corn syrup
1/2 teaspoon salt
3 to 4 tablespoons bourbon
Heat oven to 325F degrees. Combine brown sugar and 1 tablespoon granulated sugar in small bowl; set aside.
Spread bread cubes in single layer on 2 rimmed baking sheets. Bake, tossing occasionally, until just dry, about 15 minutes, switching trays from top to bottom racks halfway through. Cool bread cubes about 15 minutes; set aside 2 cups.
Whisk yolks, remaining 3/4 cup sugar, vanilla, and salt together in large bowl. Whisk in cream and milk until combined. Add remaining 8 cups cooled bread cubes and toss to coat. Transfer mixture to 13 by 9-inch baking dish and let stand, occasionally pressing bread cubes into custard, until cubes are thoroughly saturated, about 30 minutes.
Spread reserved bread cubes evenly over top of soaked bread mixture and gently press into custard. Using pastry brush, dab melted butter over top of unsoaked bread pieces. Sprinkle brown-sugar mixture evenly over top. Place bread pudding on rimmed baking sheet and bake on middle rack until custard has just set, and pressing center of pudding with finger reveals no runny liquid, 45 to 50 minutes. Transfer to wire rack and cool until pudding is set and just warm, about 45 minutes.
To make the sauce: Bring sugar, cream, butter, corn syrup, and salt to boil in deep medium saucepan, whisking until sugar dissolves. Reduce heat to medium; boil 1 minute without stirring. Remove from heat. Stir in bourbon. Cool, stirring occasionally. Spoon sauce over bread pudding and serve.