Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a large bowl, whisk together eggs, sugar, milk, whipping cream, melted butter, vanilla extract, salt, and cinnamon until smooth.
Layer the bagel pieces and chocolate chips in the greased baking dish. Carefully pour the egg mixture over the bagels, making sure every bite is well-coated. Use the back of a spoon to gently press the bagels into the custard. Let sit for 15 minutes to soak.
Bake the casserole in the preheated oven for 45–50 minutes, or until puffed, golden brown, and a knife inserted into the center comes out clean. Let the dish rest for 10 minutes before serving.
While the casserole bakes, prepare the drizzle. In a large bowl, beat the softened cream cheese and melted butter until smooth. Whisk in the powdered sugar, milk, and vanilla until the mixture is creamy and pourable.
Drizzle the cream cheese icing generously over the warm casserole, saving any extra for serving on the side.