Butter a 12x8 baking dish, and set aside.
Slice the bagels in half, and spread 2-3 tablespoons of cream cheese on half of the slices. Sandwich them together, and cut the bagels into 4 equal-sized pieces.
Arrange the bagel pieces in a single layer at the bottom of the prepared baking dish.
In a separate bowl, beat the eggs, milk, and vanilla extract until smooth. Pour the mixture over the bagels. Cover, and refrigerate overnight.
Preheat the oven to 350 degrees Fahrenheit.
In a bowl, mix together the cinnamon, butter, sugar, brown sugar, salt, and flour until it resembles coarse crumbs. Evenly spread the mixture over the bagels.
Bake for 35-40 minutes or until golden brown, and serve warm.
