Maple-Caramel Apple Clafoutis

Arrange a rack in center of oven; preheat to 400°F. Whisk together eggs and 1/2 cup of the brown sugar in a large bowl until sugar is dissolved and mixture is smooth, about 30 seconds. Whisk flour and salt into egg mixture until smooth. Pour half-and-half in a steady stream, whisking until mixture is combined. Add bourbon and vanilla, and stir once just to combine; set aside.

Core apples; cut into 1-in. thick wedges. Set aside.

Heat water, 5 tablespoons of the butter, and remaining 1/3 cup brown sugar in a 10 to 12-inch cast-iron skillet over medium. Cook, stirring until butter is melted and sugar is dissolved. Increase heat to medium-high, and bring mixture to a boil. Cook, occasionally swirling skillet, until mixture is thickened, about 2 minutes.

Add apple wedges to skillet, and cook, stirring to toss apples, until just tender and golden, about 10 minutes. Transfer apple mixture into a large heat-proof bowl. Rinse skillet to remove any sugar residue. Dry skillet well. Coat bottom and sides of skillet with 1 tablespoon of the butter. Dust buttered surfaces with powdered sugar, and tap out excess.

Stir batter once, then pour into prepared skillet. Using a slotted spoon, lift apple slices from bowl, leaving juices behind, and arrange over batter. Bake in preheated oven until puffed and deep golden brown around edges, and golden in center, 25 to 30 minutes.

While custard bakes, pour maple syrup in a deep pot with a thick bottom over medium. Bring to a boil, stirring every few minutes with a wooden spoon, 10 to 15 minutes. The syrup will start to coat the spoon, and will cool quickly into a caramel consistency. (If the mixture begins to harden like candy, it has gone too far.) Stir in remaining 1/4 cup butter until completely melted, and then add cream, stirring constantly. Return to a boil for 2 minutes. Remove from heat. Stir in salt.

Carefully remove skillet from oven, and let cool 15 minutes. (Custard will look puffy but will fall as it cools.) Drizzle with maple-caramel sauce before serving. Serve with whipped cream, if desired.