Whisk heavy cream, egg yolks, and white sugar together in a saucepan over medium heat until smooth, about 5 minutes. Remove custard from heat when it starts to simmer. Whisk in vanilla extract and cinnamon.
Arrange apple slices in the bottom of six 6-ounce ramekins. Divide caramel topping evenly over apples. Ladle custard over caramel.
Transfer ramekins to a baking dish. Pour enough warm water into the dish to come halfway up the sides of the ramekins.
Bake in the preheated oven until custard is set, 30 to 40 minutes. Remove from oven and cool to room temperature, about 1 hour. Cover with plastic wrap and refrigerate until chilled, about 3 hours.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Arrange ramekins on a baking sheet. Sprinkle 1 1/2 teaspoons brown sugar over each custard.
Broil in the preheated oven until sugar is melted and crisp, about 2 minutes.