Grease a Bundt pan with nonstick cooking spray or some softened butter. Set aside.
In a very large mixing bowl, whisk together eggs. Add milk, heavy cream, sugar, cinnamon, vanilla, and a pinch of salt. Whisk well.
Add bread cubes on top of egg-milk mixture and fold together until nearly all of the liquids have been soaked into the bread cubes. Take a few minutes to gently stir these to encourage as much of the milk mixture to soak in as possible.
Transfer bread cubes to prepared bundt cake pan. Pour any remaining egg-milk mixture over top.
Cover and refrigerate overnight, anywhere from 12 to 18 hours.
When ready to bake, remove the bundt pan from the refrigerator and let it rest at room temperature while the oven is heating.
Preheat oven to 350°F / 177°C.
Pour melted butter over bread and down sides of pan.
Bake until golden brown around the edges and cooked in the center, 40 to 45 minutes (it may take 5 to 10 minutes longer if the bake was still very cold when it went into the oven).
Let bagel bake cool in pan for 10 minutes while making glaze.
Using a standing mixer fitted with the whisk attachment or hand mixer, beat together softened cream cheese and powdered sugar (start on low and slowly increase speed). When fully combined, start slowly adding milk a little at a time until the glaze is smooth and pourable. (You may not need all of the milk.)
Turn bagel bake out on a serving platter. Drizzle glaze over top. Slice and serve warm.