6 cups apples, peeled and sliced into 1/2-inch wedges
1 teaspoon ground cinnamon
Preheat the oven to 400 degrees F (200 degrees C).
Mix eggs and brown sugar in a bowl until smooth. Whisk in flour and salt. Slowly add milk, stirring constantly until well combined. Stir in vanilla extract and set aside to rest.
Melt butter, brown sugar, and water in a 10 1/4-inch cast iron skillet over medium-high heat. Stir frequently until mixture starts to boil. Reduce heat to medium; swirl skillet, but do not stir, until mixture starts to thicken, about 2 minutes. Add apples and cinnamon. Cook and stir until apples are crisp-tender and starting to brown, 15 to 18 minutes. Remove from heat.
Stir egg mixture and pour over the apples in the skillet.
Bake in the preheated oven until edges are golden brown and custard is set, 28 to 35 minutes.