Preheat oven to 375°F. Whisk together cream, eggs, egg yolk, granulated sugar, and cinnamon in a large bowl until smooth. Stir in king cake cubes; let stand 5 minutes.
Spoon mixture into a lightly greased 11- x 7-inch baking dish, and bake in preheated oven until light golden brown and set in center, 40 to 45 minutes. Sprinkle with sparkling sugar; serve immediately with Chicory Ice Cream.